13th International Conference on the Exact Renormalization Group 2026 (ERG2026)

1 Sept 2026, 00:00 → 5 Sept 2026, 23:00 Europe/London

University of Sussex

Daniel Litim (University of Sussex), Manuel Reichert, Michael Scherer (Ruhr University Bochum), Peter Millington (University of Manchester)

13th International Conference on the Exact Renormalization Group (ERG2026)

1 - 5 September 2026,  University of Sussex, UK.

The biennial ERG conference series brings together scientists from around the world who specialise in applications of the exact or functional renormalisation group to understand physical phenomena from weak to strong coupling.  

The event has grown to cover a wide range of research areas in theoretical physics including critical and quantum critical phenomena, gauge theories, strongly correlated fermions, particle physics, model building, nuclear and statistical physics, quantum theories of gravity, non-equilibrium dynamics, machine learning and AI, and more.  

The list of invited plenary speakers include

Yuto Ashida (Tokyo)
Ginestra Bianconi (London)
Leonie Canet (Grenoble}
Laura Classen (Stuttgart)
Nicolo Defenu (Zurich)
Kevin Falls (Montevideo)
Gergely Fejös (Budapest)
Holger Gies (Jena)
Massimiliano Gubinelli (Oxford)
Igor Herbut (Vancouver)
Christopher Herzog (London)
Chris Hooley (Coventry)
Friederike Ihssen (Bochum)
Lennart Klebl (Würzburg)
Yannick Kluth (Toronto)
Benjamin Knorr (Heidelberg)
Chiu Fan Lee (London)
Tim Morris (Southampton)
Enrico Pajer (Cambridge)
Jan Pawlowski (Heidelberg)
Marc Schiffer (Nijmegen)
Fabian Rennecke (Giessen)
Vladimir Rosenhaus (New York)
Neil Turok (Edinburgh)
Lingxao Wang (Tokyo)
Christof Wetterich (Heidelberg)
Roman Zwicky (Edinburgh)

A principal goal of the conference is to foster collaboration, to enable a fruitful exchange of knowledge, ideas, and expertise, and to strengthen the communication amongst different communities and practitioners of quantum field theory. The event provides ample space to highlight recent progress and to discuss areas of wider topical interest, and new directions.

See this link for the principal conference homepage and registration.

The conference starts on Tue 1 Sep in the morning, and arrival on Mon 31 Aug is encouraged. The conference ends on Sat 5 Sep midday to allow for travel. Please notice that Mon 31 Aug is a nation-wide holiday in the UK.

Talks and Poster Session

We invite the submission of abstracts for contributed talks and poster presentations. Submissions prior to 17 May 2026 will receive full consideration.

A dedicated poster session will be held at the start of the conference with prizes for best posters sponsored by Europhysics Letters (a letter journal exploring the frontiers of physics). 

Conference Fee and Registration

The conference fee is set at 195£ (245£) for students and 310£ (360£) for non-students for registration before (after) the 1 June 26. The conference fee includes a welcome reception, conference dinner, excursion, coffee breaks, infrastructure, and more. The registration and collection of fees are organised through the Institute of Physics (IoP): Registration.

Accommodation

We have secured subsidised accommodation on campus (40£ per night), on campus B&B (78 GBP per night), and discounted rates for various hotels in the city centre. Please follow the accommodation link for details.

 

This is the first instalment of the conference in the UK. Links to previous instalments can be found here:

ERG2024 (Les Diablerets, Switzerland)
ERG2022 (Berlin, Germany)
ERG2020 (Kyoto, Japan)
ERG2018 (Paris, France)
ERG2016 (Trieste, Italy) 
ERG2014 (Lefkada, Greece)
ERG2012 (Aussois, France)
ERG2010 (Corfu, Greece) 
ERG2008 (Heidelberg, Germany)
ERG2006 (Lefkada, Greece)
ERG2000 (Rome, Italy)
ERG1998 (Faro, Portugal)

International Advisory Committee

M. Birse (Manchester), J. P. Blaizot (Saclay), L. Canet (Grenoble), B. Delamotte (Paris), A. Eichhorn (Heidelberg), T. Kunihiro (Kyoto), D. F. Litim (Sussex), W. Metzner (Stuttgart), N. Ohta (Osaka MU), R. Percacci (Trieste), M. Salmhofer (Heidelberg), N. Tetradis (Athens), C. Wetterich (Heidelberg).

 

Organising Committee

Daniel Litim (Sussex), Peter Millington (Manchester), Manuel Reichert (Sussex), Michael Scherer (Bochum).

If you have any queries, don't hesitate contacting us via <erg2026@sussex.ac.uk>.

 

Sponsors

This event is supported by 

 

Endorsements

We acknowledge the endorsement by the following IOP special interest groups:

High Energy Physics | Mathematical and Theoretical Physics | Nuclear Physics | Astroparticle Physics | Theory of Condensed Matter | Low Temperature | Biological Physics | Quantum Optics, Quantum Information and Quantum Control

 

 

Tuesday 1 September

1 Welcome

2 Unified theory of interacting Dirac fermions in two dimensions, and the dark side of the Gross-Neveu model

Gapless Dirac fermions appear as low-energy excitations in many condensed matter systems of recent interest. They are often weakly interacting, as famously in graphene, but at stronger interactions they can also acquire a gap ("mass") and exhibit many ordered ground states by going through phase transitions at which gapless Dirac fermions play a crucial role. Prime example of this occurs in the Hubbard model on honeycomb lattice at half filling, which suffers a "relativistic Mott transition" from gapless semimetal to gapped insulator, believed to be observed recently in twisted multilayers.

I will discuss the recent unification of all order parameters for Dirac systems in two dimensions based on large hidden orthogonal symmetry of free Dirac fermions. Interestingly, the unique interacting field theory that respects such an orthogonal symmetry turns out to be equivalent to the celebrated Gross-Neveu model. I will argue that, in spite of recently turning 50, this model still has a large, unexplored, and surprisingly interesting region of its coupling constant. Recent analytical and numerical results relevant to this "dark side" of the Gross-Neveu model will be presented.

Speaker: Prof. Igor Herbut (Simon Fraser University)

3 Towards First-Principles Functional Renormalization Group for Quantum Materials

In this talk, I introduce the first open-source functional
renormalization group (FRG) code for condensed matter systems: divERGe.
The development of flexible and accessible computational frameworks is
becoming increasingly important as modern condensed matter problems
continue to grow in complexity, spanning from minimal theoretical
models to realistic descriptions of quantum materials. divERGe is
designed to bridge this gap by providing a versatile platform for
implementing and applying FRG approaches across a broad range of
systems.

I will highlight the general structure of the code, its modular design,
and key interface considerations that enable efficient adaptation to
different physical problems and computational workflows. Particular
emphasis will be placed on how divERGe facilitates studies beyond
conventional single-band models, including multi-orbital and multi-
sublattice systems, as well as applications incorporating fully first-
principles-derived material parameters. This allows for a systematic
investigation of competing electronic instabilities and emergent phases
in increasingly realistic settings.

The talk will further showcase several recent applications
demonstrating the capabilities of the framework. Notable use cases
include the prediction of unconventional chiral p/d-wave
superconductivity in twisted bilayer WSe₂, the identification of nearly
nodeless extended s-wave superconductivity in twisted bilayer SnSe₂,
and the electronic origin of Pomeranchuk order in a Ti-based Kagome
metal. These examples illustrate how modern FRG techniques can provide
valuable insights into the mechanisms driving unconventional quantum
phenomena in complex materials.

Speaker: Dr Lennart Klebl (University of Würzburg)

10:30 Coffee

4 Superdiffusion and chaos from Bernoulli randomness on simple graphs

While universality on regular lattices is controlled by the Euclidean dimension, its fate on inhomogeneous structures has long remained an open question, with early work identifying the spectral dimension as the relevant parameter. In this talk, I will consider simple random graphs where long-range bonds are drawn from a Bernoulli distribution, so that the same bonds simultaneously generate superdiffusive transport and correlated quenched disorder — a situation beyond the conventional Harris and Weinrib–Halperin framework, where disorder perturbs a pre-existing clean theory. For the self-avoiding walk on such graphs, large-scale Monte Carlo simulations and a Gaussian-truncated field theory show that the long-range kinetic operator dominates under coarse-graining, restoring the clean superdiffusive Lévy universality class, yet through an irrelevance mechanism qualitatively different from the Weinrib–Halperin scenario. In contrast, in the single-particle spectral problem the same geometric randomness generates quantum-chaotic level statistics and drives a localization transition beyond the reach of Gaussian field theory, signalling the infrared relevance of higher Bernoulli cumulants. These results identify graph disorder as a distinct class of randomness, whose non-Gaussian statistics may give rise to novel universality classes.

Speaker: Prof. Nicolo Defenu

5 FRG phase diagram and superconductivity from ab-initio models of twisted WSe2

Moiré materials constitute a highly tunable platform to investigate strongly correlated phenomena. In recent experiments, superconductivity was observed in the moiré material twisted WSe2, which extends the material families of superconductors and promises to advance our understanding of this intricate many-body quantum state. Superconductivity in twisted WSe2 appears next to an interaction-induced insulator and is tunable via an external displacement field. We analyze the correlated electron phases in twisted bilayer WSe2 at hole filling -1 and twist angle 3.65 using functional renormalization group calculations and investigate the dependence on model input. The advantage of using functional renormalisation here is that it treats the different ordering tendencies on equal footing and can detect superconductivity from repulsive bare interactions. We compare the instabilities obtained from a continuum model with gate-screened Coulomb interaction and a three-orbital Wannier model with Hubbard interaction, which we derive from first principles. In both cases, we find a superconducting instability with a mixed d-wave singlet and p-wave triplet symmetry arising adjacent to inter-valley coherent spin density wave order in the phase diagram for varying displacement field and interaction strength. We argue that the pairing mechanism is consistent with inter-valley coherent spin fluctuations as pairing glue. We show that the size and critical temperatures of the pairing regime change depending on the model input, and we argue that the main difference comes from the range and quantum geometry entering the projected interaction. In particular, we obtain pairing down to zero displacement field from the Coulomb interaction within the continuum model, reconciling theory and experiment.

Speaker: Laura Classen (Max-Planck-Institut for Solid State Research)

12:00 Lunch

Parallel Session: Room 1

6 Landau damping and quantum criticality in Fermi systems from the Wilsonian RG perspective

We readdress quantum criticality of itinerant Fermi systems in dimensionality d=2 adopting the Wetterich equation as the starting point. Upon neglecting Fermi self-energy in the loop integrals of the functional RG flow, we identify a non-Fermi liquid RG fixed point and recover the features of earlier RPA-type approaches in the entire frequency range. In a subsequent step, focusing on the low-energy regime, we self-consistently include scaling of the self-energy and the Yukawa coupling. We find a generic instability of the non-Fermi liquid RG fixed point. This implies, at least at this truncation level, absence of the QCP with ordering wavevector $\vec{Q}=0$ and development of a first-order phase transition or a phase characterized by $\vec{Q}\neq 0$.

Speaker: Paweł Jakubczyk (Institute of Theoretical Physics, Faculty of Physics, University of Warsaw)

7 Quantum critical Dirac semimetals and finite-temperature effects

Interaction-induced quantum phase transitions in Dirac materials, known as relativistic Mott transitions, involve spontaneous symmetry breaking and are accompanied by a non-vanishing expectation value of a scalar order parameter. For the first time, such transitions have recently been observed experimentally in moiré Dirac materials through the tuning of the twist angle. In this contribution, we explore the chiral Ising, chiral XY, and chiral Heisenberg models at zero and finite temperature using the functional renormalization group. We show the emergence of the quantum critical fan, which allows the observation of quantum critical behavior even at finite temperatures, and facilitating thus its experimental and numerical detection. Our approach furthermore allows us to systematically describe semimetallic precondensation and the manifestation of the Mermin-Wagner theorem at finite temperature. In addition, we discuss signatures of non-Dirac-liquid behavior, analogous to non-Fermi-liquid physics near metallic quantum critical points, as well as signatures of Berezinskii-Kosterlitz-Thouless physics in the chiral XY model, connecting our work to topological phase transitions. Finally, we study the emergence of Lorentz invariance near and away from criticality, and show how the recent experimental results can be described by our approach.

Speaker: Mireia Tolosa-Simeón

8 From Bose glass to Many-Body Localization in a one-dimensional disordered Bose gas

One-dimensional interacting bosons subjected to disorder are known to possess an insulating ground state, called the Bose glass. At finite temperature, perturbative computations advocate for a crossover to a non-disordered normal fluid, but an alternative scenario was also suggested, arguing for the existence of a genuine phase transition. The resulting low-temperature insulating phase is then akin to the Many-Body Localized (MBL) phase, first introduced for fermions.
To settle this debate, we develop a field-theoretical approach leveraging the Functional Renormalization Group (FRG). At zero temperature, we find a new non-perturbative fixed point, the approach to which contains information on the low-energy excitations of the system. We then turn to finite temperature effects, discussing various crossovers to the normal fluid phase, where disorder still plays an important role at finite length and time scales. Finally, we point out how a modification of our approximations leads to a different scenario for the low-temperature physics of the system, and put forward a hypothesis linking it to MBL.

Speaker: Vincent Grison (Sorbonne Université)

9 Dynamics in quantum random-field systems: localization or activation?

We study disorder-dominated quantum models, including Ising-like random-field systems and equilibrium pinned elastic-manifold problems, near their zero-temperature critical regimes. We provide an explicit field-theoretic calculation supporting the fluctuationless fixed point scenario, in which the infrared critical fixed point is classical and quantum fluctuations enter through a dangerously irrelevant temperature-like scaling variable. This establishes a close correspondence with classical random-field models, whose critical dynamics is commonly formulated in terms of Langevin relaxation and is dominated by activated processes over barriers that grow as a positive power of the length scale.

We derive the resulting extremely slow, activated dynamical scaling from the interplay between disorder and quantum fluctuations, and connect this mechanism to the renormalization-group flow of the dynamical kernel and of the longest relaxation time. In the quantum problem, the activated form of the scaling should be interpreted as arising from tunneling between competing configurations, rather than from thermal activation over effective barriers in configuration space. Related mechanisms may also be relevant at other disorder-dominated quantum critical points, including the superfluid-Bose-glass transition in disordered bosons, disorder controlled transitions of relativistic semimetals, such as the ballistic semimetal to diffusive metal transition, and strongly disordered quantum magnets in which disorder cumulants control the infrared scaling.

Speaker: Ivan Balog (Institute of Physics, Zagreb)

Parallel Session: Room 2

10 Strongly coupled four-fermion fixed points in four dimensions

Four-fermion interactions are important in many areas of particle physics, from effective descriptions of weak interactions and QCD to parametrisations of new physics in SMEFT or HEFT. In this talk I demonstrate that four-fermion interactions may develop strongly coupled UV fixed points in four dimensional QFTs. Contrary to weakly coupled expectations, their high energy limit may be (near-) conformal, with radically altered scaling behaviour due to large anomalous dimensions. The idea will be illustrated in a purely fermionic model of the Gross-Neveu type using the toolbox of the large-N expansion. I will show that the model, suitably extended with higher-derivative and eight-fermion interactions, is renormalisable to all orders in the expansion, with physical predictions being fully determined in terms of three parameters. I will further discuss exact RG running and operator scaling in the near-conformal UV regime, including from the perspective of functional renormalisation, as well as implications for effective theory and model building.

Speaker: Charlie Cresswell-Hogg

11 Chiral Lagrangian as a proxy for ASQG

The existence of an ultraviolet (UV) fixed point in the renormalization group (RG) flow of gravity provides a non-perturbative route to renormalizing gravity, that is Asymptotically Safe Quantum Gravity. Evidence for such a UV completion has been found in a variety of settings, including higher-derivative gravity theories and gravity–matter systems. However, despite its apparent robustness, it remains an open question whether this UV completion corresponds to the true, metric-based quantum theory of gravity.

On the other hand, chiral perturbation theories share several common features with gravity, such as perturbative non-renormalizability and the nonlinear nature of their interactions. As effective low-energy descriptions of strong interactions, their UV completion is known to involve different degrees of freedom, namely quarks and gluons.

In this talk, I explore the possibility that chiral theories exhibit a UV fixed point along the RG flow. I will show that, despite their similarities with gravitational theories, these models do not admit an asymptotically safe UV completion within a quartic-derivative truncation. This result is consistent with the existence of an alternative UV completion and highlights that asymptotic safety is not a generic property, but rather a feature of a limited class of special systems.

Speaker: Francesco Del Porro (Niels Bohr Institute)

12 Renormalizability and UV behavior of 5D gauge theories

The idea of supplementing the number of spacetime dimensions has long been deemed as one of the potential extension of the Standard Model, as it provides powerful tools to explain some of its shortcomings. One example of higher-dimensional formulations are asymptotic grand unified theories (aGUTs), for which the couplings do not meet at a high scale, but instead flow together towards a fixed point in the UV. Although the higher-dimensional dynamics push the theories into a nonpertubatively renormalizable regime, they can be thought of as fundamental in the context of the asymptotic safety scenario. Using these techniques, we focus on five-dimensional gauge theories and check the existence of fixed points, thus ensuring a good behavior in the UV. Additionally, the presence of both bulk and localized divergencies is investigated, with the purpose of shedding light on the renormalization status of such theories.

Speaker: Anca Preda (Lund University)

13 RG fixed points from outer automorphisms and goofy transformations

I will show how the existence of an outer automorphism (Out) provides a sufficient condition for the existence of an RG fixed hyperplane (fixed point, separatrix) in the renormalization group (RG) flow of a Quantum Field Theory (QFT). This gives a systematic way to derive non-perturbative all-order constraints on the RG beta functions and provides the mathematical underpinning of 't Hooft's technical naturalness argument. The beta function constraints and associated RG fixed hyperplanes can be computed non-perturbatively without resorting to perturbation theory. Besides well known exact symmetries, I will also discuss the recently discovered so-called goofy transformations. Even though goofy transformations are, by definition, explicitly broken by kinetic terms, they can give rise to all-order stable RG fixed points. I will use the Out constraints to explain why this is the case. Since goofy transformations can control bare scalar mass parameters and scalar portal couplings, they provide a new class of solutions to the electroweak scale hierarchy problem.

Speaker: Andreas Trautner (CFTP, IST, University of Lisbon)

Parallel Session: Room 3

14 The $\theta$-vacuum from functional renormalisation

We study topological properties of a quantum mechanical system with $U(1)$-symmetry within the functional renormalisation group (fRG) approach. These properties include the vacuum energy structure and the topological susceptibility. Our approach works with a complexification of the flow equation, and specifically we embed the original symmetry into the complex plane, $U(1)\rightarrow \mathbb{C}$. We compute the effective potential of a given topological sector by restricting ourselves to field configurations with given generalised non-trivial Chern–Simons numbers. The full potential is directly constructed from these sector potentials. Our results compare well with the benchmark results obtained from solving the corresponding Schr\"odinger equation.

Speaker: Yuepeng Guan (Jilin University)

15 Conformal Symmetry as an Organizing Principle for the Derivative Expansion

The derivative expansion is a central approximation scheme within the functional renormalization group, yet its convergence is often hindered by a strong dependence on the choice of regulator.
In this talk, we argue that this limitation originates from the incomplete realization of conformal symmetry at criticality within standard projection procedures. To address this issue, we construct a symmetry-consistent projection onto the derivative expansion in which conformal constraints are explicitly enforced at the critical fixed point. The resulting scheme significantly reduces regulator dependence and exhibits an improved convergence pattern, while also lowering computational complexity.
We implement this approach for the three-dimensional Ising universality class at fourth order and benchmark the results against conventional sixth-order calculations as well as other established methods.
Our findings highlight conformal symmetry as a key organizing principle for functional renormalization group truncations and provide a systematic pathway toward more accurate and efficient approximations in critical phenomena.

Speaker: Gonzalo De Polsi

16 Modified Forward Scattering and Unitarity in Matter Chern-–Simons Theory

Recently, the familiar $S$ matrix form $S=1+iT$ and crossing rules were challenged in Chern--Simons theories coupled to bosonic or fermionic matter. In the planar large-$N$ singlet channel, the proposed modifications restore unitarity by changing both the forward identity contribution and the crossing relation obeyed by the $T$ matrix. In this talk, we present a direct perturbative calculation of $2\to2$ matter scattering through order $1/k^2$ at finite $N$. We provide the first finite-$N$ perturbative verification of the conjectured forward contribution beyond the planar singlet channel, and show that it restores unitarity.

Speaker: Max Uetrecht (TU Dortmund University)

17 New approach to OPE coefficients from the FRG

In a quantum field theory, the product of two operators in the short distance limit can be expressed as a sum of operators multiplied by functions (when inserted in any correlation function).
This so-called operator product expansion (OPE) is of fundamental importance in the study of conformal field theories (CFTs) in two and higher dimensions. There, due to the the conformal symmetry, the OPE of two operators is uniquely determined by a set of numbers, the OPE (or Wilson) coefficients [1].

The determination of these coefficients has generated recent interest, with approaches from conformal bootstrap [2] or the fuzzy sphere [3]. FRG has been able to determine with great quantitative precision c112, the leading order coefficient of the OPE of \phi and \phi, for the 3d O(N) models and the Ising model in dimensions 2<=d<=4 [4]. The method used, however, cannot be directly applied to other coefficients.

Here, we present a method that can be used to determine arbitrary coefficients, which relies on finding the fixed point for the flow equation in presence of a source coupled to a composite operator, as recently proposed in Refs. [5].

[1] Di Francesco, Mathieu, and Sénéchal, Conformal Field Theory (Springer New York, 1997).
[2] Kos, Poland, Simmons-Duffin, and Vichi. J. High Energy Phys. 08, 036 (2016).
[2] Rose, Pagani, and Dupuis, Phys. Rev. D 105, 065020 (2022).
[3] Zhu, Han, Huffman, Hofmann, and He, Phys. Rev. X 13, 021009 (2023); Hu, He, and Zhu, Phys. Rev. Lett. 131, 031601 (2023).
[4] Delamotte, De Polsi, Tissier, and Wschebor, Phys. Rev. E 109 064152 (2024); Cabrera, De Polsi, Wschebor, Phys. Rev. E 111 054126 (2025).

Speaker: Félix Rose (LPTM, CY Cergy Paris Université)

15:00 Coffee

Poster presentations: 1-min slide show

18 TBC

Speaker: Mr David Dullaway (University of Sussex)

19 Constructing UV-critical hypersurfaces using machine learning

We provide a novel computational method for constructing the UV-critical surface along the lines of [arXiv:2403.08541]. Using physics informed neural networks to learn flow invariants, we recover the UV-critical surface all at once. The method is successfully applied to a UV-critical surface for an asymptotically safe scalar-tensor theory, where we predict the IR effective field theory. We argue that these types of networks are highly efficient computational tools extracting physics from flow equations.

Speaker: Stijn Hennissen (Radboud University)

20 Resurgence in Ward–Schwinger–Dyson Equations for QED

Resurgence in Ward–Schwinger–Dyson Equations for QED

Edwyn Tecedor (1)(3), Marc Bellon (1)(2), Redamy Perez-Ramos (1)(3)
(1) Sorbonne Université LPTHE , CNRS (2), IPSA (3), Paris, France

Perturbative expansions in quantum field theory are divergent, with coefficients exhibiting factorial growth. Resurgence analysis provides a systematic framework to decode this growth and extract non-perturbative information via the Borel–Laplace resummation and alien calculus [1]. The Ward–Schwinger–Dyson (WSD) approach yields exact, regularisation-independent equations for the Green functions, compatible with the renormalisation group, and has been shown to provide a natural setting for resurgent analysis in the φ³₆ model [2, 3].

We extend this programme to massless QED in four dimensions. The presence of two coupled propagator equations, the Ward–Takahashi identity constraining the vertex [4], and the infrared structure of 4D, each introduce new features with respect to the scalar case. We set up the WSD system for the QED vertex using momentum differentiation and infrared rearrangement, reducing the determination of the anomalous dimension to the evaluation of a single-scale loop integral whose Mellin residue encodes the full resurgent structure. The non-trivial Dirac algebra of the theory is handled systematically and contributes a numerator that modifies the pole structure of the Borel transform with respect to φ³₆.

We present the current state of this ongoing work and discuss the open questions that remain on the road to a full resurgent analysis of QED.

[1] J. Ecalle ,Les fonctions résurgentes, Algèbres de fonctions résurgentes. Publ. Math. Orsay 81.05 (1981).
[2] M. P. Bellon, E. I. Russo, Ward–Schwinger–Dyson equations in φ³₆ quantum field theory, Lett. Math. Phys. 111 (2021), arXiv:2007.15675.
[3] M. P. Bellon, E. I. Russo, Resurgent analysis of Ward–Schwinger–Dyson equations, SIGMA 17 (2021), arXiv:2011.13822.
[4] J. C. Ward, Renormalization theory of the interactions of nucleons, mesons and photons, Phys. Rev. 84 (1951).

Speaker: Edwyn Tecedor (LPTHE - Sorbonne Université)

21 Many-body correlations in Floquet steady-states: Frequency-resolved renormalization group of the driven Anderson impurity

We introduce a functional renormalization group framework formulated directly in the Floquet steady-state that systematically incorporates frequency-dependent interaction effects. By retaining the frequency structure of the two-particle vertex up to second order in interaction strength, our approach provides controlled access to dynamical response functions and nonequilibrium transport in driven, interacting systems. Using the periodically driven single-impurity Anderson model as a paradigmatic example, we benchmark our results against state-of-the-art Floquet Green’s function methods and find quantitative agreement for finite-frequency observables up to intermediate interaction strengths. Remarkably, we also show that static properties are often captured reliably by much simpler approximations, suggesting practical pathways for modeling driven quantum materials. We demonstrate that, although periodic driving of the dot strongly broadens the Kondo resonance through inelastic scattering, it leaves the many-body Kondo cloud largely intact. This robustness suppresses Floquet replicas of the Kondo peak and leads to a partial persistence of Kondo pinning, highlighting the resilience of emergent many-body correlations under local periodic driving.
Finally, to extend our framework beyond impurity models we present first proof of concept results by implementing FRG using quantics tensor trains (QTT), taking advantage of scale separation in the frequency and momentum degree of freedom to reduce memory requirements. Utilizing tensor cross interpolation (TCI) one can construct the compressed representation directly from adaptive function evaluations, bypassing instantiation of the full tensor. Internal integrations can now be performed efficiently as tensor contractions, while convolution integrals can be executed via the discrete quantum Fourier transform represented as low-rank matrix product operators.

Speakers: Dominik Chudy (RWTH Aachen University), Jan Herre (RWTH Aachen University)

22 Weyl Gauged Gravity

Scale-invariant extensions of gravity, particularly quadratic gravity, offer a compelling setting due to their perturbative renormalizability and potential asymptotic freedom. Formulated in Weyl geometry, these models naturally allow physical energy scales, such as the Planck mass, to emerge dynamically through a spontaneous symmetry‑breaking mechanism, which in turn enables the recovery of an Einstein–Hilbert action in the infrared and provides a natural framework to accommodate the Standard Model.
We study the renormalization group flow of quadratic gravity in Weyl geometry using the background field formalism. We compute the one‑loop effective action and derive the beta functions for the independent quadratic couplings, analyzing how the Weyl connection modifies propagators and interaction vertices. This allows us to explore the theory's ultraviolet behavior and assess the prospects for a UV‑complete extension of Einstein gravity. Our preliminary results obtained with the heat-kernel method will be extended and shared in an upcoming paper by computing the Feynman diagrams directly.

Speakers: Fabrizio Chicconi (University of Pisa, INFN), Dr Luca Parente (University of Pisa, INFN)

23 One symmetry, multiple avatars: U(1) in Asymptotically Safe Gravity

Coupling gravity to the U(1) gauge sector induces higher-order gauge interactions that can be investigated using functional renormalization group (FRG) techniques. Within the framework of Asymptotic Safety, previous studies have shown that the existence of ultraviolet (UV) completions for these induced interactions can impose constraints, for example, on the strength of gravitational interactions at high energies. This leads to the so-called “Weak Gravity Bound”. In this work, we study the impact of distinguishing between different pure-matter and gravity-matter avatars of the induced interactions. These are known to follow different renormalization group flows within truncated settings. We analyze how introducing these distinct avatars modifies the fixed-point structure of the system. By examining the stability properties of the resulting UV fixed points, we also assess the predictivity of the theory as well as the extent to which universality of couplings is restored at infrared scales.

Speaker: Juan Fernandez Molinero (Radboud University)

24 Multicritical fixed points from functional renormalisation

We investigate multicritical points in O(N) symmetric scalar field theories in various dimensions. Using functional renormalisation to leading order in a derivative expansion, we find analytical and numerical results for critical and multi-critical points. In the large-N limit, we investigate local and global fixed points, and the availability of lines of fixed points analogous to the BMB phenomenon for tri-critical theories in 3D. For suitable choices of the regularisation, we find analytic results for the critical potential, and demonstrate that the spectrum of eigenperturbations is given in terms of generalised Laguerre polynomials.

Speaker: Iason Vakondios

25 Can the Radiation Era be Extended all the way to the Bang?

It turns out that imposing reflecting boundary conditions at the Big Bang singularity itself is sufficient to explain the CMB Power spectrum without the assumption of an exotic epoch preceding radiation era. However, there are well known problems with starting the Universe in a radiation dominated phase such as the horizon problem, overproduction of dark matter, and thermalization of gravitons. In this talk I will explain how quadratic curvature terms in the gravitational action can avoid these issues while imposing constraints on the Weyl squared coupling. We will also discuss how the Big Bang singularity can be avoided in a theory with Weyl symmetry and discuss a toy model QFT that looks close to the Standard Model which is anomaly free and has a well-defined UV completion on a curved background. We use the exact renormalization group to study this Weyl anomaly.

Speaker: Vatsalya Vaibhav (University of Edinburgh)

26 Resurgence and FRG Perspectives in Strong-Field QED

In this work, we investigate aspects of resurgence in quantum electrodynamics (QED) in strong external background fields. Resurgence provides a framework for understanding how divergent perturbative series can be related to non-perturbative contributions. In particular, we study the vacuum polarization tensor and the mass operator, or electron self-energy, in a self-dual background field in Minkowski spacetime. This topic is especially relevant in strong-field regimes, where conventional perturbative expansions may break down, as suggested by the Ritus-Narozhny conjecture. In addition, we explore how this investigation can be connected to ideas from the functional renormalization group. From this viewpoint, the vacuum polarization tensor and the electron self-energy are related to two-point functions obtained from functional derivatives of the scale-dependent effective action, allowing QED in external backgrounds to be studied within a scale-dependent framework.

Speaker: Mr Gabriel Weigert (Friedrich-Schiller-Universität Jena)

27 On the Structure of the Fermion Sector in the Asymptotically Safe Standard Model

Quantum gravity impacts Standard Model particles through effective interactions generated by renormalization. These appear as SMEFT operators, which correct Standard Model dynamics at energies between the electroweak symmetry breaking scale and the Planck scale. As a step to predicting SMEFT coefficients from asymptotic safety, we investigate the flow of a representative collection of fermionic operators under gravitational fluctuations. We find a mechanism that can make these operators relevant based on symmetry arguments. This allows us to categorize SMEFT operators by their potential of providing a free parameter to the flow of the Asymptotically free Standard Model.

Speaker: Moritz Gessner (Universität Heidelberg)

28 Conformal Invariance Constraints in the Functional Renormalization Group

In the critical regime of statistical-mechanical systems, thermodynamic quantities follow power laws as functions of a control parameter due to the effective interaction of the system at all scales. This universal behavior is associated with scale invariance and, in many cases, extends to conformal invariance, that is, invariance under the most general group of transformations that preserve angles, which in turn imposes additional constraints on the theory.

The functional renormalization group provides an appropriate framework to study this regime, and the derivative expansion is one of its most successful approximation schemes. At finite order, however, the derivative expansion does not exactly preserve conformal invariance, leading to violations of the corresponding Ward identities.

In this work, we study these violations in the three-dimensional Ising universality class, described by an effective scalar $\phi^4$ theory, within the derivative expansion of the functional renormalization group up to order $O(\partial^4)$, including composite operators. This makes it possible to derive new conformal constraints and to follow how the same constraint evolves at successive orders of the approximation scheme, providing a test of the convergence of the derivative expansion from the viewpoint of symmetry restoration.

We also show that conformal information can be used directly, not only as a diagnostic of the approximation, but also to improve it. Incorporating conformal constraints directly into the truncation leads to a significant improvement in the estimate of critical exponents and to a reduced residual dependence on the regulator. This highlights the connection between regulator optimization, conformal symmetry, and the accuracy of functional renormalization group approximations.

Speaker: Jorge Ibañez (Universidad de la República (UdelaR))

29 Chiral Quantum Phase Transition in Moiré Dirac Materials at finite density

Chiral quantum phase transitions in Dirac materials at finite density: Strong enough interactions induce a semimetal-to-insulator transition in Dirac materials, which can be viewed as the solid-state analogue of the chiral phase transition in quantum chromodynamics. Moiré Dirac materials such as twisted bilayer graphene offer a new opportunity to study this transition because they facilitate tuning the effective interaction via a twist angle. Motivated by this, we explore the quantum phase transition of a (2+1) dimensional Dirac material at T = 0K which spontaneously develops a gap that breaks an Ising symmetry. It is still an open question what is the structure of the phase diagram at finite chemical potential. To explore it, we study a Gross-Neveu-Yukawa model for the phase transition using both a mean-field theory. Interestingly, we find an intermediate state between semi-metal and insulator where a inhomogeneous solution appears to be stable. Future research steps include the study of this problem through functional Renormalization Group.

Speaker: Ana García-Page (Max-Planck-Institut for Solid State Research)

30 Probing Conformal Windows with Perturbation Theory

Interacting fixed points of the renormalisation group play a central role in determining whether or not quantum field theories exhibit conformal behaviour. In this work, we investigate the conformal windows of weakly coupled fixed points in gauge-matter theories, through a systematic loop-by-loop analysis of perturbative beta functions in the large $N$ Veneziano limit. Our focus is on two complementary settings: the infrared (IR) Banks-Zaks fixed point in asymptotically free gauge theories and the ultraviolet (UV) fixed point of the Litim-Sannino model, which is a gauge-Yukawa theory. For the Banks-Zaks fixed point, we analyse the gauge beta function up to five loop order and study how successive perturbative corrections modify the extent of the IR conformal window. For the Litim-Sannino fixed point, we introduce a projection method that reduces the multi-coupling system to an effective single-coupling beta function, thereby enabling a computationally rigorous investigation of the UV conformal window up to four loop order. For both models, we place a particular emphasis on fixed point mergers as a mechanism that could delimit the conformal window. Our results allow for a comparative assessment of the convergence properties of both models, providing an insight into the reliability and perturbative consistency of their respective conformal windows.

Speaker: Nahzaan Riyaz (University of Sussex)

31 Spatial Coarse-Graining Impedes the Ability to Classify Message-Passing Algorithms

Supporters of the Bayesian Brain Hypothesis argue that the brain maintains a generative model of the environment and inverts this model to infer the states of the world. Message-passing is one class of algorithms that performs this computation tractably. While there is some evidence that the brain uses specific forms of message-passing, such as mean-field variational inference, other algorithms, such as Thouless-Anderson-Palmer message-passing, remain plausible candidates but have yet to be thoroughly considered. In this study, we investigate the measurement requirements for comparing message-passing algorithms as alternative explanations of data. We examine how the spatial precision of neural recordings would affect the ability to determine which message-passing algorithm the brain implements. Even with exact coarse-graining procedures using the renormalization group, we were not able to identify the ground-truth implemented by individual neurons. Thus, fine-grained measurements may be necessary to draw conclusions about how the brain could implement Bayesian inference through message-passing.

Speaker: Carter Goldman (University of Sussex)

32 Gauge-Invariant and Background-Indepedent Quantum Gravity

In Quantum Gravity, the regulator breaks diffeomorphism symmetry and background independence. In this talk, we reinstate gauge invariance and background independence by a field redefinition at every renormalisation group step and discuss the properties of the resulting Reuter fixed point. Moreover, we show improved stability results for simple gravity-matter systems.

Speaker: Paul Philip Sprenger (Institute for Theoretical Physics, Heidelberg University)

33 Universal Thermodynamics of Two-Dimensional Bose Gas: a Non-Perturbative Renormalization Group Approach

We investigate the thermodynamics of the two-dimensional Bose gas within the framework of the non-perturbative functional renormalization group (NP-FRG) and quantum phase transitions. The existence of a quantum critical point in the vacuum-superfluid transition implies that thermodynamic functions can be expressed as universal scaling functions [1]. Furthermore, using the flow equations of the NP-FRG derived from the second-order derivative expansion, we demonstrate how to determine these universal quantities and characterize the low-temperature phase, which exhibits algebraic order and Berezinskii-Kosterlitz-Thouless (BKT) physics [2]. From the NP-FRG flow equations, we show how to calculate the gas's equation of state and its superfluid density, thereby fully characterizing its thermodynamics : from Tan's contact to sound velocities. Our calculations exhibit remarkable agreement with experimental observations. To illustrate this, we compare our results to recent cold atoms experiments [3,4]. We also demonstrate that the method is robust by comparing different approximation.

[1] A. Rançon and N. Dupuis, Phys. Rev. A 85, 063607 (2012).
[2] P. Jakubczyk, N. Dupuis and B. Delamotte, Phys. Rev. E 90, 062105 (2014).
[3] T. Yefsah, R. Desbuquois, L. Chomaz, K. J. Gunter and J. Dalibard, Phys. Rev. Lett. 107, 130401 (2011).
[4] P. Christodoulou, M. Gałka, N. Dogra, R. Lopes, J. Schmitt and Z. Hadzibabic Nature 594, 191–194 (2021).

Speaker: Yaniss Rabahi (PhLam laboratory)

34 On black-hole scalarization: strong breaking of black-hole uniqueness and constraints from asymptotically safe gravity

Black-hole uniqueness is expected to break in theories beyond General Relativity. This breaking can take a particularly strong form, if several branches of black-hole solutions beyond the Kerr solution coexist. We find an example of a theory that exhibits such strong breaking, where, at fixed couplings, two different scalarization mechanisms types coexist for spinning black holes. We test such theory through a more fundamental approach: we ask if this theory is compatible with asymptotic safety. This results in a phenomenological tool to discriminate between different quantum gravity theories. It turns out that it can be compatible only for extremely small black holes, of Planck mass size. This makes asymptotic safety and scalarization in astrophysical black holes incompatible.

Speaker: Lidia Marino (ITP-Heidelberg)

35 Scalar Matter in Lorentzian Quantum Gravity

We study the interplay of scalar matter with quantum gravity in the Lorentzian signature using the recently developed spectral fRG. The spectral fRG is based on the Callan-Symanzik cutoff, which acts as a scale-dependent mass and preserves the Källén-Lehmann spectral representation, in combination with dimensional regularisation. In this setup, we compute the impact of N_S minimally coupled scalars on the gravitational UV fixed point and on the transverse-traceless graviton spectral function. Scalar matter increases the strength of the fixed-point Newton coupling, and beyond N_S = 21, the fixed point is lost. A similar behaviour was found in previous Euclidean studies. Remarkably, scalar matter provides a strictly positive and gauge-independent contribution to the graviton spectral function, leaving the property of positivity intact.

Speaker: Rowan Packer (University of Sussex)

36 Analytic results in Asymptotic Safety

I am presenting analytic results on momentum-dependent gravitational and gravity-matter correlation functions in Asymptotic Safety. I will discuss their complex-analytic structure, and results on scattering cross sections.

Speaker: Benjamin Knorr (Heidelberg University)

37 From Functional to Ricci Flows: Asymptotic Safety in Perturbation Theory

Evidence for the existence of a UV fixed point in quantum gravity is usually derived using the functional renormalization group. In this talk, I discuss how this fixed point can be found solely using perturbation theory, provided one adopts a suitable renormalization scheme that retains the relevant physics. While the FRG achieves this naturally, I will discuss alternative methods tailored to a perturbative formulation, such as modifications of minimal subtraction in dimensional regularization, or the Ricci flow in quantum gravity. Similarly to the FRG, these methods yield a one-loop fixed point in four-dimensional quantum gravity. I close by discussing the implications of these findings and the connection to FRG results.

Speaker: Yannick Kluth (University of Toronto)

Poster presentations

38 Two-Component Bose Mixtures: Mean-Field Theory and Functional Renormalisation Group

We investigate a two-component Bose mixture with repulsive intra- and interspecies interactions in two and three spatial dimensions. In three dimensions, we analyse the global structure of the phase diagram, the order of the phase transitions, and the associated universality classes using mean-field theory and the functional renormalisation group. The system exhibits four distinct phases: a normal phase, two single-component condensed phases, and a phase characterised by the simultaneous condensation of both components. Mean-field theory captures the principal phase structure, while the functional renormalisation group incorporates long-wavelength fluctuation effects, primarily leading to quantitative shifts of the phase boundaries. In two dimensions, we focus on the role of thermal fluctuations, which preclude true long-range order at finite temperature and place the system in the regime of Berezinskii–Kosterlitz–Thouless physics. Our results show how dimensionality and fluctuation effects shape the stability of condensate phases in multicomponent Bose systems.

Speaker: Oskar Stachowiak

39 Critical behavior of isotropic magnets with screened dipolar interactions

Dipolar interactions play an important role in the critical behavior of isotropic magnets. While the microscopic physics is usually dominated by short-range exchange interactions, dipolar interactions are strongly relevant in the RG sense due to their long-range nature, leading to a crossover from O(N) universality towards the dipolar fixed point, as pointed out by Aharony and Fisher in the early 1970s. The situation is much less clear in the presence of screening effects, which for example appear in antiferromagnets. In this regime, the long-range part of the interaction is suppressed and the surviving short-range term is canonically marginal. We investigate the fate of this term at classical and quantum phase transitions within a functional renormalization group approach. In accordance with previous perturbative results, we find it to be marginally irrelevant and provide a first estimate of the corresponding critical exponent. We discuss implications for rotational symmetry breaking in arbitrary isotropic systems, as well as consequences for systems with lower symmetry, like cubic magnets or electronic nematicity.

Speaker: Max Fornoville (Max Planck Institute for Solid State Research)

40 Negative diffusion in the Functional Renormalization Group flow for the Quark-Diquark Model

We investigate the Quark-Diquark Model (QDM) with the functional Renormalization Group (fRG) in the local potential approximation. In a recent work [arXiv:2510.01066 [hep-ph]], problems were reported in applying this method at low temperatures and large quark chemical potentials, which were attributed to numerical artifacts. In this work, we trace the origin of these problems to the occurrence of a negative diffusion coefficient during the fRG flow of the derivative of the effective potential, leading to strong oscillations of the latter quantity. We show that negative diffusion is a model feature and not a numerical artifact, propose a regularization scheme which introduces a hyperdiffusion term to remove these oscillations, and demonstrate its effectiveness for studies of the phase diagram of the QDM. Regularizing the negative diffusion in the fRG flow is particularly important to reliably study phenomena such as color superconductivity and inhomogeneous phases, which might emerge in the high-density, low-temperature region of the QCD phase
diagram.

Speaker: Johannes Pöplau

41 Self-consistent quark-meson spectral functions

We present a self-consistent, manifestly Lorentz-invariant computation of real-time quark and meson spectral functions in the two-flavour Quark-Meson model, performed directly on the Minkowski axis using the spectral functional renormalisation group with emergent composites. The present work hosts two qualitative improvements over other spectral functional works so far. The first one is the inclusion of all-order scatterings via a full effective potential. The second one is the resolution of higher order decays and, in particular, the $\pi \to 3\pi$ scattering threshold - the lowest kinematically accessible channel for the pion. Moreover, the sigma mode exhibits a Breit-Wigner resonance reflecting its instability against decay into two pions.

Speaker: Konrad Kockler (Institut für Theoretische Physik, Universitat Heidelberg)

42 Analytically continued FRG for dissipative open quantum systems

Euclidean approaches such as the functional renormalization group (FRG) have been abundantly and successfully used to study the universal static critical behavior of various physical systems near continuous phase transitions. For the study of critical dynamics, on the other hand, one usually relies on real-time methods. This work illustrates the applicability and limitations of using Euclidean systems and the analytically continued FRG (aFRG) to study critical dynamics. In particular, we formulate a dissipative open quantum system in Euclidean spacetime, in the spirit of the Caldeira-Leggett model. Consecutively, we investigate the dynamic critical behavior and compare to real-time results for the dynamic universality class of Model A (according to the classification by Halperin and Hohenberg).

Speaker: Patrick Niekamp (JLU Giessen)

43 Cosmology from asymptotically safe Proca theories

Effective field theories for cosmology offer a powerful framework to investigate the dynamics of space–time and address longstanding open puzzles. In this work, we initiate a programme to analyse the ultraviolet completion of vector–tensor quantum field theories within the asymptotic safety paradigm, focusing on generalised Proca theories with a vector condensate. This enables us to assess whether a consistent fundamental UV completion exists and to constrain the set of viable infrared scenarios. Using the non–perturbative functional renormalisation group, we identify several fixed points, including Proca–type candidates, and, among them, a particularly remarkable one with four relevant directions: two associated with gravity and two induced by matter. This provides evidence for the non–perturbative renormalisability of vector–tensor theories. We further outline how the resulting UV critical surface constrains late–time cosmology.

Speaker: Carlos Pastor Marcos (Institute for Theoretical Physics (ITP), Heidelberg University)

44 Symmetry breaking in the Nambu-Jona-Lasinio Model using the FRG

Investigation of supposedly non-renormalisable four-fermion interactions using the FRG reveals non-trivial fixed points that recover predictivity. Scale-symmetry breaking and mass generation can be seen in Gross–Neveu theory, which involves only 'scalars' (​ψbarψ). We extend these ideas to the Nambu-Jona-Lasinio model, which includes a 'pseudo-scalar' (ψγ5barψ) such that there is an overall U(1)xU(1) global symmetry. The flow of this theory is equivalent to Gross–Neveu, but the appearance of non-analytic operators calls for clarification, which we achieve via partial bosonisation. This makes breaking of the global U(1) symmetry manifest, which may open a route to studying pion-like Goldstone modes in a more exact setting.

Speaker: Freddie Matthew King (University of Sussex)

45 Probability distribution of order parameter in O(N) models

We investigate the probability distribution of the order parameter in the O(N) model, with a focus on its behavior near criticality. Characterizing the full distribution provides direct insight into fluctuations and universal features of the system.

On the analytical side, we employ the Functional Renormalization Group (FRG), which enables a non-perturbative treatment of critical fluctuations and allows access to the scale dependence of the effective action. This approach yields predictions for the shape and scaling behavior of the order parameter distribution across different regimes.

Complementing the analytical study, we perform numerical simulations using the Wolff cluster algorithm, which efficiently reduces critical slowing down in O(N) models. From these simulations, we extract the order parameter distribution and compare it with FRG predictions.

We interpret the resulting distributions as a generalization of the Central Limit Theorem to systems with strongly correlated degrees of freedom. In this setting, critical correlations give rise to non-Gaussian universal distributions, extending the classical CLT paradigm beyond independent or weakly correlated variables.

Speaker: Lovro Šaravanja (Institute for Physics)

46 Spontaneous symmetry breaking in a relativistic Yukawa theory with Luttinger fermions

We investigate spontaneous symmetry breaking in a relativistic Yukawa theory with Luttinger fermions that exhibits self-organized criticality. Within the LPA' approximation, we numerically resolve the renormalization group flow of the full effective potential. We follow the flow from the symmetric phase, characterized by a partial fixed point, into the symmetry-broken phase. Featuring an RG-marginal scalar mass parameter, the flow displays logarithmically slow running toward symmetry breaking. We compute the mass spectrum, including the fermionic gap and the scalar excitation, quantitatively. Furthermore, in the large-$N_f$ limit, we analyze the full effective potential analytically and systematically compute corrections to this approximation.

Speaker: Tim Lukas Eckert (FSU Jena)

47 Composite-field tree expansions of 1PI vertices

We present an exact functional reformulation of one-particle irreducible (1PI) vertex functions in terms of derivatives of a composite-field effective action. The construction is based on an inverse Legendre transformation relating the standard 1PI effective action to an extended effective action that depends explicitly on collective fields.

Functional differentiation of this transformation generates exact tree expansions for arbitrary 1PI vertices, where propagators and interaction vertices are replaced by correlators and renormalized couplings of composite fields. Different choices of composite operators reproduce known vertex decompositions, including formulations related to dynamical bosonization and Hubbard–Stratonovich transformations, while naturally extending them to higher-order vertices and more general interacting field theories.

For theories with at most quartic interactions, we further show that the non-bare part of the 1PI effective action can be represented entirely in terms of two- and three-point Green’s functions through a Legendre transform of the 3PI Luttinger–Ward functional. The resulting framework provides a unified perspective on nonperturbative vertex reorganizations and suggests new truncation strategies for functional renormalization-group and $n$PI approaches.

Speaker: Oleksandr Sulyma

48 Scaling regimes of shallow water turbulence

We study the shallow water model, which is a simplified model obtained from the Navier-Stokes equations by imposing the existence of a free surface and assuming the vertical height of the fluid to be small compared to the horizontal dimensions. This model allows to describe turbulent cascades in oceans near the coast or in highly stratified fluids. Moreover, the shallow water equations can be fruitfully used to benchmark ideas and techniques to be later applied to the full 3-dimensional problem of surface gravity waves. Different regimes and scaling laws are observed in experiments and direct numerical simulations, suggesting a rich phase diagram depending on the parameters of the model. Existing theoretical analyses are mainly based on the statistical closure known as Wave Turbulence, which is inherently perturbative and cannot access all the different regimes. In this work, we use the Functional Renormalization Group to explore the phase diagram of the shallow water model beyond the perturbative limit. We compute in particular the energy spectrum to characterize the different cascades and scaling regimes depending on the model parameters.

Speaker: Gregorio Tibone (Côte d'Azur University, INPHYNI)

49 Generative diffusion model with inverse renormalization group flows

The renormalization group (RG) framework, which establishes a connection between a microscopic model at short distances and its coarse-grained counterpart at larger scales, has been a pivotal tool for understanding many-body phenomena across vastly different scales, ranging from elementary particles to condensed matter. Central to the RG's success is its multiscale nature, enabling systems with distinct short-scale behaviors to exhibit similar patterns at macroscopic scales.

On another front, recent advances in machine learning have positioned diffusion models [1, 2] as one of the most prominent examples of generative models, achieving a great success across various domains, including computer vision, audio synthesis, and point cloud generation. Nevertheless, diffusion models have so far largely overlooked the inherent multiscale structures of natural data, and their slow generation process remains a bottleneck for expanding their applications to important domains in physics [3].

In our work [4], we introduce a novel class of generative diffusion models inspired by the concept of the RG, which leverage the multiscale properties of natural data to realize efficient and high-quality data generation. Specifically, we establish a connection between the flow equations in the RG framework and the convex diffusion equations underlying diffusion models. This connection allows us to construct a diffusion model that generates data in a coarse-to-fine manner by reversing the RG flows, thereby naturally incorporating the multiscale structures in natural data. To validate the effectiveness and versatility of our approach, we apply the model to real-world problems in two distinct domains: protein structure prediction and image generation. Our numerical results demonstrate that the RG-based diffusion models consistently outperform conventional models across all tested datasets, enhancing sample quality and/or accelerating sampling speed by an order of magnitude.

In the poster presentation, we illustrate the theoretical formulation of the RG-based diffusion model and demonstrate the numerical results that support the validity of the model. The framework of our scalable RG-inspired approach to data generation is rather general and would bear a close connection to machine learning approaches for analyzing, e.g., (Boltzmann) distributions in quantum and classical field theories.

[1] J. Sohl-Dickstein, E. Weiss, N. Maheswaranathan and S. Ganguli, Proc. of the ICML, 2256 (2015).
[2] J. Ho, A. Jain, and P. Abbeel, Adv. In NIPS 33, 6840 (2020).
[3] K. A. Dill, S. B. Ozkan, M. S. Shell, and T. R Weikl, Annu. Rev. Biophys. 37, 289 (2008).
[4] K. Masuki and Y. Ashida, arXiv:2501.09064 (2025).

Speaker: Kanta Masuki (The University of Tokyo)

50 Mass scale hierarchies in a Yukawa model with Luttinger and Dirac fermions from self-organized criticality

We introduce a Yukawa model where a scalar boson interacts with both
relativistic Luttinger fermions and Dirac fermions.
The Luttinger-Yukawa sector exhibits features similar to self-organized
criticality (SOC) which provides for a natural scale separation between an
initial UV scale and the scale of spontaneous symmetry breaking and mass gap
generation. We observe that the SOC mechanism accompanied by a partial fixed
point is stable under the inclusion of (gauged) Dirac fermions. In turn, the
SOC mechanism exerts a strong influence on the renormalization flow of the
Dirac sector, naturally inducing a strong mass hierarchy with naturally small
Dirac masses. The model provides a first example that the relativistic SOC
mechanism can generate two vastly different scales without any fine-tuning of
initial parameters.
Coupling the Dirac fermions to a non-abelian gauge field, the SOC mechanism
generically drives the Dirac Yukawa coupling into a regime where its infrared
flow is governed by that of the gauge coupling.

Speaker: Yunxin Ye (FSU Jena)

51 Non-perturbative news from the conformal window

Dynamical symmetry breaking plays a crucial role in mass and scale generation. In QCD-like theories, its dependence on the number of fermion flavours determines the phase structure and the transition to the conformal regime. In this work, we employ the functional renormalisation group and the generalised flow equation to compute non-perturbative corrections, including momentum dependencies and field invariants essential for an adequate realisation of the global symmetry. As a consequence, the critical gauge coupling required for dynamical chiral symmetry breaking acquires a strong dependence on the number of flavours and increases sharply at $N_f^\textrm{crit}\simeq 7.30$ for $N_c=3$. This establishes a new picture of the conformal phase transition that challenges Miransky/BKT scaling and the existence of walking regimes, favours a first-order quantum phase transition, and points towards a critical region with exotic dynamics and symmetric fermion mass gaps.

Speaker: Alvaro Pastor Gutierrez (RIKEN iTHEMS)

52 Non-Renormalization of $\pi_1$-Characters under Finite ERG Transformations on Multiply Connected Configuration Spaces

We formulate finite exact renormalization group (ERG) transformations on a multiply connected configuration space $Q$ by using the universal covering map $\pi:\widetilde Q\to Q$ and the Deck transformation group $\Gamma\cong\pi_1(Q,q_0)$. Following the broad definition used by Igarashi, Suzuki, and Sonoda, an ERG transformation is treated as a linear integral transformation acting on Boltzmann factors. In this formulation, a finite ERG transformation is represented by an integral kernel $K_{\Lambda,\Lambda'}$ between two cutoff scales $\Lambda\leq\Lambda'$, rather than by its infinitesimal flow equation. The construction uses Dowker's covering-space method, where kernels on a multiply connected space are obtained from kernels on the universal cover and characters of the fundamental group. Let $e^{\widetilde S_t[\widetilde q]}$ be a cutoff-dependent Boltzmann factor on $\widetilde Q$, transforming under Deck transformations by a character $\chi:\Gamma\to\mathbb C^\times$. If the ERG kernel and the measure are invariant under Deck transformations, then the transformed Boltzmann factor has the same character $\chi$. Thus, the sector labeled by the $\pi_1$-character is preserved under finite ERG transformations. This gives a finite-kernel formulation of the non-renormalization of the $\pi_1$-character. We also derive the Gaussian ERG kernel on the universal cover from the scaling relation for the normal-ordering generating functional and describe the constraint on $\chi$ imposed by normalization on $Q$.

Speaker: Taichi Tanaka (Nihon University)

53 A tale of scales in Asymptotically Safe Quantum Gravity

Asymptotically safe quantum gravity has shown remarkable success when coupled to matter, notably yielding a successful postdiction of the top quark mass when the quantum gravity scale is identified with the Planck scale, a natural choice in a fundamental realization of Asymptotic Safety. This success raises the possibility that, even if not fundamental, asymptotically safe gravity may emerge as an effective description within a more fundamental theory. In such a scenario, the notion of scale becomes central.
Starting from the postdiction of the top-quark mass, we explore different notions of physical scales, investigating how the regime of validity of Quantum Field Theory connects to the fixed-point scale, the species scale, and the scale of a potential underlying theory. We further analyze how this interplay depends on the matter content, revealing a nontrivial and surprising structure.

Speaker: Francesco Ferrarin (University of Copenhagen, Niels Bohr Institute)

54 The moat regime under magnetic fields

We investigate the Quark–Meson Model at finite temperature and chemical potential in the presence of an external magnetic field. Emphasis is placed on the effects of (inverse) magnetic catalysis on the structure of the phase diagram. In particular, we analyze how strong magnetic fields modify the emergence and geometry of the so-called moat regime, where nontrivial dispersion relations signal the onset of spatially modulated behavior.

Speaker: Justin Mauldin (Goethe University Frankfurt)

55 Computing the Bubble Nucleation Rate with Functional Renormalisation Group Methods

Cosmological first-order phase transitions generate a stochastic background of gravitational waves (GWs), a measurement of which would signal physics beyond the Standard Model. A crucial quantity that enters the computation of the GW power spectrum is the bubble nucleation rate, which is accessible from the underlying QFT. At small coupling, the rate can be computed in perturbation theory. Alternatively, functional renormalisation group methods can be used to access the nucleation rate regardless of coupling strength. We extract the nucleation rate from the $k = 0$ quantum effective action by a suitable reconstruction of the barrier in the non-analytic convex effective potential. A benefit of this approach is that all quantum fluctuations are integrated out, and the regulator vanishes at $k = 0$. This poster charts the various techniques we have employed and some preliminary results.

Speaker: Rory Phipps (University of Sussex)

ERG 2026 Poster Slide.pdf

17:30 Fish & Chips break

56 Poster session

Wednesday 2 September

57 Dense QCD and the moat regime

QCD is expected to have a rich phase structure at finite density. However, owing to strong coupling and sign problems, only little is known from first principles. The functional renormalization group allows for direct access to dense QCD matter based on microscopic quark-gluon dynamics. Model studies suggest the existence of inhomogeneous/crystalline phases at large density. The moat regime, where the static energy of bosonic excitations is minimized at nonzero momentum, encodes spatial modulations in the system and is hence a precursor for such phases. After introducing QCD from an FRG perspective more generally, I discuss the physics of the moat regime and the possibilities for its experimental discovery through heavy-ion collisions.

Speaker: Fabian Rennecke (University of Giessen)

58 Existence of IR fixed points in the QCD chiral transition

I will review recent developments concerning the possibility of a second-order chiral transition in the zero quark mass limit. Within the local potential approximation, using a phi^6 truncation, fixed points are found spanning the entire range of flavour numbers. I will discuss potential problems with this ansatz and review how the approach could be extended to global fixed-point potentials. I will also briefly comment on the N_c = 2 scenario.

Speaker: Gergely Fejos (Eötvös University Budapest)

59 Gravitational Form Factors, Conformal Symmetry and the Conformal Window

I will review gravitational form factors and their connection to the energy-momentum tensor, with emphasis on their pressure interpretation and conformal symmetry. I will then discuss the conformal window and some (old) open questions concerning the transition between conformal and chirally broken phases. If time permits, I will illustrate these ideas with applications to my own work, including the interpretation of the $\sigma$ meson as a dilaton—the pseudo-Goldstone boson associated with spontaneously broken conformal symmetry.

Speaker: Roman Zwicky (Edinburgh University)

10:30 Coffee

60 Gravity from Entropy

Gravity is derived from an entropic action coupling matter fields with geometry called Gravity from Entropy action [1]. The fundamental idea is to relate the metric of Lorentzian spacetime to a quantum operator, playing the role of a renormalizable effective density matrix and to describe the matter fields topologically, according to a Dirac-Kähler formalism, as the direct sum of a 0-form, a 1-form and a 2-form. While the geometry of spacetime is defined by its metric, the matter fields can be used to define an alternative metric, the metric induced by the matter fields and curvature. The proposed Gravity from Entropy (GfE) action is associated to a Lagrangian given by a novel geometric quantum relative entropy (GQRE) between the metric of spacetime and the metric induced by the matter fields and curvature which capture the entanglement between geometric degrees of freedom of spacetime. The modified Einstein equations obtained from this action reduce to the Einstein equations with zero cosmological constant in the regime of low coupling. By introducing the G-field, which acts as a set of Lagrangian multipliers, and interpreting it a physical and measurable field, the proposed entropic action reduces to a dressed Einstein-Hilbert action with an emergent positive cosmological constant only dependent on the G-field. The obtained equations of modified gravity remain second order in the metric and in the G-field. Interestingly the GfE action when calculated on Schwarzschild metric allows us to derive from first principles the area law for black holes with large Schwarzschild radius [2]. Further exploration of the GfE cosmology reveals further aspects of the GfE thermodynamics reconciling the second principle of thermodynamics with the decrease of the QGRE and thus possibly with the emergence of non-uniform local structures [3].
A canonical quantization of this field theory could bring new insights into quantum gravity and the outstanding problem of its renormalization.

[1] Bianconi, G., 2025. Gravity from entropy. Physical Review D, 111(6), p.066001.
[2] Bianconi, G., 2025. The quantum relative entropy of the Schwarzschild black hole and the area law. Entropy, 27(3), p.266.
[3] Bianconi, G., 2026. Thermodynamics of the gravity from entropy theory. Physical Review D, 114(2), p.024042.

Speaker: Prof. Ginestra Bianconi (Queen Mary University of London)

61 Asymptotically safe quantum gravity: functional and lattice perspectives

Asymptotically safe quantum gravity might provide a UV complete description of nature, governed by scale-invariance realized at an interacting RG fixed point. In this talk, I will introduce Dynamical Triangulations as a tool complementary to functional methods, to explore this scenario. I will give an overview on the status of asymptotic safety from lattice studies, and focus on recent studies of matter correlators on these fluctuating lattices. On the one hand, these correlators serve as a probe of the underlying geometry and provide crucial insights into the quantum nature of geometry. On the other hand, they also allow to extract physical information, e.g., the mass anomalous dimension, and hence serve as an important bridge to functional studies. There, such critical exponents have been recently studied to high precision by resumming higher-order operators. Hence, recent progress in the study of matter correlators with functional and lattice methods pave the way towards quantitative comparison of both methods, and hence to robust, method independent insights into the quantum nature of spacetime.

Speaker: Marc Schiffer (Radboud University)

12:00 Buffet Lunch

Parallel Session: Room 1

62 $d \geq 4$ gravitational vacua and black hole thermodynamics from $2D$ dilaton theories

$2$-dimensional dilaton theories play a central role in discussions of black holes in a variety of approaches to classical and quantum gravity. In this talk I will present a unified framework for black hole thermodynamics of $d$-dimensional static black holes with spherical, toroidal or compact hyperbolic horizon topology satisfying $g_{tt}g_{rr}=-1$ in Schwarzschild gauge by considering the reconstruction of generic such black holes as solutions to integrable $2$-dimensional effective dilaton theories, and thereby as gravitational vacuum solutions to an extended notion of $d$-dimensional quasi-topological gravity. I will illustrate that the generating function determining $f(r) = -g_{tt}$ in the integrated equation of motion provides the mass in a first law of thermodynamics which can be derived for any such black hole by an application of Wald's Noether charge formalism.

Speaker: Johanna Borissova (Imperial College London)

63 Entanglement and renormalization-group flow

I discuss the entanglement entropy for a free scalar field within a spherical region in various gravitational backgrounds (flat, de Sitter and anti-de Sitter space, the Einstein universe). In the first part I focus on the structure of the divergences. Universal coefficients are determined for ultraviolet and infrared divergent terms. In the second part I discuss the use of the finite part of the entropy for the calculation of a c-function in 1+1 dimensions and an a-function in 3+1 dimensions.

Speaker: Nikolaos Tetradis (National and Kapodistrian University of Athens (GR))

64 How Sensitive is Cosmic Inflation to Quantum Corrections? An ERG Approach.

In this talk, I will present a non-perturbative framework that allows to track the dynamics of slow-roll inflation while consistently incorporating quantum corrections, based on an alternative functional renormalisation group (RG) approach. I will guide you through the derivation of a set of coupled Friedmann-RG flow equations governing the joint evolution of spacetime, the inflaton field, and its effective potential. Applying this formalism to α-attractor E-models, I will show that the RG flow induces a dynamical destabilisation of the inflationary trajectory, leading to a premature termination of slow roll. Remarkably, the resulting predictions bring α-attractors into full agreement with the latest ACT data without introducing new physics beyond a consistent quantum-corrected treatment of the inflaton dynamics.

Speaker: Lucien Heurtier (King's College London)

65 The axion coupling accelerates the Universe through \cPT-symmetric phases

The conjecture by two of the authors (N.E.M. and S.S.) that a \cPT-symmetric phase plays a role in understanding singular renormalisation group (RG) flows for a Chern-Simons (CS) gauge theory of axions, has been reexamined and significantly improved.
We have used the more complete Wetterich equation, which includes gravitational couplings in a systematic way from the start, to understand the emergence of this phase. The singular structure of the RG flows has persisted on including gravitational-couplings, thereby offering further support to the conjecture that \cPT -symmetric phases of (repulsive) gravity characterise string-effective CS gravitational theories, where the axion is the massless string-model independent axion, which can also play a role of a totally-antisymmetric torsion degree of freedom. This has suggested a novel interpretation of the currently observed acceleration of the expansion of the Universe in terms of such a phase at large (cosmological) scales.

Speaker: Prof. Sarben Sarkar (King's College London)

66 Prospects for scalar-tensor cosmology in asymptotically safe quantum gravity

Scalar-tensor theories are ubiquitous in cosmology. Asymptotic safety offers a guiding principle to significantly shrink the available theory space. At the same time, cosmological observables provide a stringent test of the asymptotic-safety paradigm. Focusing on Horndeski models of dark energy, I show how simple models fail to meet both observational constraints and constraints from asymptotic safety. With many observations still unaccounted for, I conclude with a perspective on the rich road ahead.

Speaker: Fabian Wagner (Heidelberg University)

Parallel Session: Room 2

67 Thermal precondensation and its appeareance in gauge-fermion theories

Precondensation is a peculiar phenomenon in phase transitions, characterised by the occurrence of a condensate only over a finite range of length scales. It is closely connected to the emergence of domains, pseudo-gapped phases and spatial inhomogeneities in equilibrium. In this talk, I will discuss its occurrence in gauge-fermion theories in the chiral limit, close to the thermal chiral phase transition. We further show that the precondensation regime becomes increasingly pronounced and extends over a wider temperature range as the number of fermion flavours is increased. We analyse the underlying dynamics which is shared by a broad class of fermionic systems, ranging from condensed matter to high-energy physics. Specifically, we discuss the potential relevance of this phenomenon for physics beyond the Standard Model.

Speaker: Alvaro Pastor Gutierrez (RIKEN iTHEMS)

68 Functional Renormalization Group Flows and Gauge Consistency

We consider quantum electrodynamics with chiral four-Fermi interactions in the functional renormalization group approach. In gauge theories, the functional flow equation for the effective action is accompanied by the quantum master equation that governs the underlying gauge symmetry. Beyond perturbation theory, fully gauge-consistent solutions are very difficult to obtain. By including the lowest-order correction to the photon two-point function, we use dressed nonperturbative photon propagators in the flow equation as well as the quantum master equation. We show that the 1PI effective action with the new prescription satisfies both equations within our truncations. We also discuss the phase structure in terms of the gauge and four-Fermi couplings based on a numerical solution of the system.

Speaker: Katsumi Itoh (Niigata University)

69 The Fate of Chiral Gauge Theory

The infrared structure of gauge theories with chiral fermions remains largely unexplored. In this work we investigate the Bars-Yankielowicz class using the functional renormalisation group, building on recent developments in gauge-fermion systems that provide clear criteria for confinement and dynamical symmetry breaking. We show that two distinct phases arise: one exhibiting both confinement and symmetry breaking at small numbers of colours, and another characterised by confinement without symmetry breaking in the large-colour limit. The latter realises a novel regime, opening the possibility of exotic spectra and phenomena that can now be studied within a systematic framework.

Speaker: Hao-Lin Li (Sun Yat-Sen University)

70 Diquark Properties from First Principles

Diquarks, correlated quark-quark pairs carrying net color charge, play a key role in both baryon structure and dense quark matter. In this talk I will present results for the vacuum properties of the scalar diquark in a self-consistent and first-principles approach to QCD. Using the functional renormalization group, in particular dynamical hadronization, I will show how the high energy quark and gluon degrees of freedom can be smoothly integrated resulting in a low-energy description in terms of pions, sigma-meson and diquarks. I will show, through direct analytic continuation of the flow equations, that our approach predicts a scalar diquark bound state, supporting the quark-diquark picture of the nucleon.

Speaker: Ugo Mire

71 Functional Renormalization of QCD in 1+1 dimensions

We study QCD in 1+1 dimensions focusing on meson formation in the vacuum. Utilizing a mass-like Callan-Symanzik regulator, we investigate the flow of the four-quark vertex in a Fierz complete basis. The couplings diverge in the point-like limit, signaling bound state formation. We progress with resolving some momentum dependencies by invoking a Hubbard-Stratonovich transformation. For heavy quarks, the non-relativistic limit enables us to include the full momentum dependence and all emergent mesonic degrees of freedom. Highlighting the relation to the quantum mechanical two-body problem, we provide explicit expressions for their propagator, space-dependent fields and Yukawa (quark-meson) couplings.

Speaker: Eric Oevermann (Friedrich Schiller University Jena)

Parallel Session: Room 3

72 Informational renormalization group

Renormalization group (RG) flow has been discussed widely from high energy physics to statistical mechanics. However, the connection between many-body RG and continuum RG such as Wilsonian RG and functional/exact RG is not always clear. Moreover, once we consider a finite system, the RG process becomes approximate although several independent proposals have exist in the condensed matter community. In this talk, we discuss an information theoretic (re)interpretation of RG flow based on Haar random averaging. This enables us to generalize and unify the RG process from discrete to continuum and finite to infinite systems. This talk is based on work in preparation with Teruaki Nagasawa (Kanazawa University).

Speaker: Takato Mori (Rikkyo University)

73 Exploring multi parameter optimization in FRG

Adopting the principles of minimal sensitivity we analyze, using the Wetterich Morris RG flow equations for various truncation schemes, the critical exponents of the 3-dimensional Ising universality class.

Speaker: Gian Paolo Vacca (INFN - Bologna section)

74 Non-Gaussian statistics of the order parameter across a continuous phase transition

The Ising model at criticality is a paradigmatic example of random variables displaying strong correlations at all scales. In the high and low temperature phases, the collective properties of the system are described by the standard (Gaussian) central limit theorem. In contrast, at the critical point separating the two phases, the fluctuations are non-Gaussian and are captured by a scale-invariant and universal asymptotic probability distribution. From a physicist's point of view, the emergence of such a probability distribution is understood using the renormalization group, which effectively describes the behavior of coarse-grained random variables.

In this talk, I will discuss the extension of this problem to quantum systems, using the probability distribution of the order parameter as an example of a non-trivial observable displaying non-Gaussian fluctuations at criticality. The observation of such non-Gaussianity in a recent ultracold-atom experiment will also be discussed.

Speaker: Adam Rançon (Université de Lille)

75 Universal Crossover in the Three-Channel Charge Kondo Model at High Transparency

Quantum impurity models are key platforms for studying strong electronic correlations and can be realized with high precision in quantum-dot experiments. While the low-transparency (weak-coupling) regime is well understood—particularly using the Numerical Renormalization Group—the opposite limit of highly transparent contacts has remained largely unexplored.

In this talk, I show how the functional renormalization group (FRG) provides a controlled description of the highly transparent regime. In the three-channel charge Kondo model, the FRG reproduces known universal low-energy results (obtained from conformal field theory) and captures the full crossover from high to low energies. Our results establish the FRG as a powerful nonperturbative tool for quantum impurity systems in previously inaccessible regimes.

Speaker: Mr Nicolas Paris (LPTMC Sorbonne Université)

76 The Adjoint Field as an Influence Map: Sensitivity Analysis of FRG Flows

The functional renormalization group (FRG) recasts the flow of the effective action as an initial-value problem in RG "time," which for O(N)-type models can be written as a nonlinear fluid-dynamic conservation law for the field-space derivative of the potential. Physical observables - the IR vertex functions $\Gamma^{(2n)} = \partial_\sigma^{2n-1}u|_{\sigma=0}$ - are highly localized functionals of a solution that develops steep restoration fronts and near-singular structure during the flow. This makes the accurate, certified extraction of vertices genuinely hard, and it raises a broader question that is usually answered only by expensive parameter scans: how do the extracted observables depend on the many choices that enter an FRG calculation — the regulator (cutoff) shape function, the UV initial data, the truncation, and the discretization itself ?

We argue that the adjoint method is the natural and unifying tool for these questions. The adjoint field $\lambda(\sigma,t) = \delta J/\delta u(\sigma,t)$ is the exact sensitivity of any chosen observable $J$ to a perturbation of the state at every RG time, obtained from a single backward integration of the transposed flow — at the cost of essentially one extra solve, independent of the number of parameters. Its interpretation is physical, not merely numerical: $\lambda$ is an influence map that reveals which regions of field space and which RG scales actually determine a given IR vertex, quantifies the RG "freeze-out" of each observable, and — crucially — differentiates $J$ with respect to any ingredient of the flow at once.

We demonstrate the framework on the O(N) model. First, as goal-oriented error control and adaptivity: the dual-weighted-residual estimator built from $\lambda$ yields a certified, exact-solution-free error bound with effectivity $\approx 1$, and - by exposing that a residual plateau under mesh refinement signalled a consistency rather than a resolution error- directly diagnosed and motivated the cure for a persistent bias in the higher vertices. Second, and more generally, we show how the same adjoint gives, at negligible additional cost, the gradient of IR observables with respect to the regulator shape function and the UV initial condition — turning regulator-(in)dependence studies and optimized-cutoff searches from brute-force scans into a single sensitivity computation, and opening the door to gradient-based regulator design and inverse/data-assimilation problems in FRG.

Speaker: Ashutosh Dash

15:40 Coffee

77 Stochastic observables and constructive RG

Scale-dependent observables are the basic concept of the renormalization group. I will present a recent formalisation of this idea in the context of the probabilistic approach to Euclidean QFT and how it gives naturally rise to various structures, in particular local diffusions called Wilson-Ito diffusions which generalise the ideas of Polchinski’s RG and also RG for stochastic equations.

Speaker: Massimiliano Gubinelli (University of Oxford)

78 Diffusion Models as Stochastic Quantisation

Generative diffusion models — the engine behind much of modern image and video synthesis — turn out to admit a transparent physical reading: the forward process is a Langevin diffusion that washes out structure, while the reverse, score‑driven process reconstructs configurations from noise, realising a stochastic quantisation à la Parisi–Wu with the learned score playing the role of the drift derived from an effective action.
Building on this correspondence, I will present our recent results from the DM‑QFT collaboration on generative sampling for lattice field theory: scalar theories in two and three dimensions including their critical regions, group‑preserving diffusion for U(N)/SU(N) gauge fields, and ongoing progress. I will emphasise Expandability, Exactness and Efficiency, and close with the road ahead QCD.

Speaker: Dr Lingxiao Wang (RIKEN)

79 Renormalisation Group approach to General Relativity

In this talk I will discuss a new approach to classical general relativity.
Currently, most analytical methods to general relativity are inherently perturbative, while Numerical Relativity remains computationally expensive. I will present a middle path: an exact renormalization group (RG) equation for classical gravitational systems. The equation correctly reproduces the Post-Minkowskian expansion, while also easily recovers the 1PN two-body action, bypassing the need for complex three-graviton vertex calculations. I will then show how the equation can be derived from the classical limit of the Polchinski equation, demonstrating its exactness. This establishes the exact RG as a powerful new tool for tackling strong-field dynamics in gravity.

Speaker: Dr Kevin Falls

Thursday 3 September

Parallel Session: Room 1

80 Asymptotically safe Standard Model

I will review developments on the asymptotically safe Standard Model, in which an ultraviolet completion of the Standard Model with gravity may give rise to emergent structures in the Standard-Model couplings, which compare well with observed structures.

Speaker: Astrid Eichhorn

81 Fixed points of the renormalisation group flow the CKM and PMNS matrices : CP violation in the Standard Model and beyond

The RG flow of the CKM matrix in the Standard model will be presented and the fixed points found. There are six fixed points, associated with the elements of the symmetric group of three objects, $S_3$. A proof is given that these are fixed points to all orders in perturbation theory and even non-perturbatively. The analysis is equally applicable to the PMNS matrix in the leptonic sector, with three sterile right-handed Dirac neutrinos.

Speaker: Prof. Brian Dolan (Dublin Institute for Advanced Studies)

82 Near-criticality of the neutrino sector of the Standard Model

Neutrinos oscillate with large mixing angles. Dirac neutrino masses are small
compared to the other Standard Model fermions and a near-degenerate mass spectrum
is compatible with experimental data on neutrino masses. However, large mixing is not
radiatively stable in the near-degenerate case. Here, we find that the Standard Model lies
close to a transition between a phase with large and a phase with vanishing mixing angles.
This gives rise to a bound on neutrino masses: given the measured mass differences, the
electron neutrino mass cannot be larger than approximately 1 eV within the Standard Model.
Beyond the Standard Model, in the presence of asymptotically safe quantum gravity, the
bound is lowered to ∼ 0.6 − 0.7 eV, pushing the transition tantalizingly close to the current
experimental bound by the KATRIN experiment.

Speaker: Zois Gyftopoulos (Heidelberg University)

83 Quantum gravity contributions to the gauge and Yukawa couplings in proper time flow

We derive quantum gravity contributions to the beta functions of the gauge and Yukawa couplings of a matter theory using the Schwinger proper-time flow equation. Working in the Einstein-Hilbert truncation, we investigate the gauge-fixing and regulator dependence of the corresponding renormalization group equations. We quantify the sensitivity of our results on unphysical parameters by evaluating the gravitational correction to the running matter couplings at the interactive fixed point of gravity and we compare our findings with existing determinations in alternative schemes. We finally confront the derived contributions with the typical size they should assume to generate observable low-scale predictions in the Standard Model and in several scenarios of new physics.

Speaker: Daniele Rizzo (KBFI-Tallinn)

Parallel Session: Room 2

84 Rethinking Dimensional Regularization in Critical Phenomena

We show that it is possible to use dimensional regularization (DR) beyond the usual $\varepsilon$-expansion in the context of renormalization group (RG) calculations in Critical Phenomena.
Based on this fact, we propose a new functional RG scheme - Functional Dimensional Regularization (FDR) - and apply it to a scalar theory in three dimensions.
We compute the critical exponents of the Ising universality class directly in $d=3$ under various typical approximations.
The method that emerges combines the agility typical of DR with the generality proper of functional RG.
Moreover, at a given order of approximation, FDR seems to provide faster convergence and better estimates than other functional RGs.

Speaker: Alessandro Codello (Ca' Foscari)

85 Functional Dimensional Regularization for O(N) Models

The novel functional dimensional regularization (FDR) scheme has proven capable of yielding results that are competitive with the state-of-the-art in the computation of critical exponents in $d=3$, while also reproducing those from the $\varepsilon$-expansion for the Ising and other universality classes. In this work, we show that this is not a mere coincidence: by applying the scheme to the $O(N)$ universality class, we explicitly derive the flow equations and obtain critical exponents that are comparable to those obtained with higher-order non-perturbative approaches. In this case, FDR retains the features already highlighted in previous works -- namely, its efficiency and rapid convergence.

Speaker: Piero Beretta (Facultad de Ingeniería. Universidad de la República)

86 Perturbatively Exact Fixed Points in Three Dimensions

I will report about recent progress to systematise the search for non-trivial fixed points in three dimensions. I revisit the stability of the UV fixed point in purely scalar theories using perturbation theory. I will discuss how the results are compatible with FRG, and address an old controversy in the literature. Furthermore, scalar-fermionic theories are investigated up to four-loop order, and a novel class of IR fixed points under strict perturbative control is identified.

Speaker: Tom Steudtner

87 Mass generation at a fixed point: A Functional Renormalization Group Study of the tricritical O(N) model in d=3 and N=∞

Renormalization group (RG) fixed points are commonly associated with scale invariance and a divergent correlation length. We show that this connection can fail in the tricritical O(N) model in three dimensions in the limit N→∞. Revisiting the line of fixed points identified by Bardeen, Moshe, and Bander, we use the functional renormalization group to clarify the mechanism leading to mass generation at its singular endpoint (the BMB fixed point). We demonstrate that the generated mass is nonuniversal and originates from the nonanalytic structure of the effective potential. We show that the critical exponent ν which takes the value ν=1/2 along the regular part of the BMB line, that is, for 0≤λ<λBMB, jumps to ν=1/3 on the singular part of this line with the BMB FP, corresponding to λ=λBMB, being the pivotal point between these two regimes. We also show how its singular potential emerges dynamically along the renormalization flow.

Speaker: Dr Shunsuke Yabunaka (ASRC, JAEA)

Parallel Session: Room 3

88 Density functional theory of renormalization group in nuclear matter

The density functional renormalization group (density-fRG) is proposed to investigate the density fluctuations within the functional renormalization group approach, which allows us to quantify the medium effect and study physics of high densities. This method is applied to the nucleon-meson effective field theory, also known as the Walecka model, to study the properties of nuclear matter at high baryon densities. It is found that both the attractive and repulsive nucleon meson interactions are screened by the high density medium, which results in a stiffer equation of state (EoS) of nuclear matter in the regime of $\rho_0 \lesssim \rho \lesssim 2.5 \rho_0$, then a softer EoS when $\rho \gtrsim 2.5 \rho_0$. Here $\rho_0$ denotes the saturation baryon density of symmetric nuclear matter. Furthermore, a new phenomenon called the locking of Fermi surface is found. In the locking of Fermi surface the effective energy of quasi-nucleon is always close to the Fermi surface, which are both running with the renormalization group scale.

Speaker: Prof. Wei-jie Fu (Dalian University of Technology)

89 Precondensation and inhomogeneous instabilities in high-density QCD

QCD at large densities exhibits a moat regime in the scalar-pseudoscalar sector. The resolution of its dynamics is pivotal to access the onset of new phases, including the potential critical endpoint of QCD.
I report on a first self-consistent analysis of this regime, using the first-principles functional renormalisation group approach to QCD.
Mapping out the moat regime, we find a potential inhomogeneous instability at baryon chemical potential $\mu_B \gtrsim 600$MeV on the chiral crossover line.
I discuss the stability of this instability together with the closely connected phenomenon of precondensation, which can be probed in a natural manner using the fRG.

Speaker: Franz Richard Sattler (University Bielefeld)

90 Pion Distribution Amplitudes from Functional QCD

We present the first functional QCD calculation of the pion distribution amplitude (DA) using the large-momentum effective theory in the functional renormalization group (fRG) framework. With only the strong coupling and current quark masses as input, we compute the quasi-DA from first-principles QCD correlation functions. By pushing the pion momentum up to $P_z = 4.5\ \mathrm{GeV}$, the quasi-DA becomes fully saturated, rendering the extrapolation uncertainty to the light-cone limit negligible. The resulting second moment $\langle \xi^2 \rangle_\pi = 0.267$ is significantly smaller than existing lattice-LaMET determinations and lies in a range consistent with other nonperturbative approaches.

Speaker: Chuang Huang (Heidelberg University, ITP)

91 FRG Constraints on Diquark Pairing: Implications for Color-Superconducting Quark Matter

Astrophysical observations of massive neutron stars and compact-object mergers increasingly point toward the presence of deconfined quark matter at high densities. In such environments, quarks are expected to form color-superconducting diquark pairs. Their properties are typically modeled within effective theories, where parameter fixing remains challenging due to the absence of diquarks as asymptotic states.

In this work, we employ a functional renormalization group (FRG) framework to self-consistently construct a vacuum low-energy effective description in which scalar diquarks dynamically emerge. Applying the resulting constraints to cold and dense quark matter, we find a sizable diquark gap in the chirally restored phase, along with a speed of sound significantly exceeding the conformal limit. These results suggest that color superconductivity could have observable consequences, provided that quark matter is realized in neutron stars.

Speaker: Bernd-Jochen Schaefer

10:20 Coffee

Parallel Session: Room 1

92 Spectral Functions of Lorentzian Quantum Gravity

Using modern functional renormalisation adapted for theories in Lorentzian signature, and enhanced by new symmetry conditions to account for underlying Ward identities, we derive and solve flow equations directly for the Källén-Lehmann representation of propagators. Consistent results are found for several sets of renormalisation conditions yielding normalisable spectral functions for the graviton and the scalar graviton mode, in agreement with effective theory in the infrared. All resulting spectral functions are compatible with causality and unitarity. They provide direct access to the full quantum propagators and the quantum effective action up to quadratic order in the curvature. Renormalisation schemes that simplify the RG flows are identified, which paves the way for the computations of non-perturbative scattering amplitudes directly in Lorentzian signatures.

We also present several extensions of this framework. This includes the first Lorentzian spectral flow for the Newton coupling, and graviton spectral flows in schemes with improved control over diffeomorphism symmetry breaking. Implications for convergence of spectral flows are also indicated.

Speaker: Gabriel Assant

93 Unitarity at all scales: Towards 2-to-2 scattering of scalars in Asymptotically Safe Quantum Gravity.

Asymptotically safe quantum gravity provides a UV completion of metric quantum gravity, with and without matter. This is achieved via scale invariance in the strongly coupled regime, entailing finiteness at all scales. Compared to the existence of the scaling symmetry, the study of the unitarity of the theory is still in its infancy. In this talk, I present the asymptotically safe scattering amplitude of two-to-two scalar fields.
Focusing on the mediated amplitude, we use modern functional renormalisation group methods to obtain non-perturbative momentum-dependent results for the resummed scalar-graviton vertex and propagators.
Together with reconstruction and analytic continuation techniques. These are corredated by the gravitational contribution to the contact amplitude, whose we resum directly in Lorentzian signature.
This allows us to study the non-perturbative amplitude and cross-section.
The cross-section is an observable of the theory; it is compatible with GR at small energies, and it respects unitarity in the UV.

Speaker: Angelo Portas Chiesa (University of Sussex)

94 Understanding IR divergences in higher derivative theories

In higher derivative (HD) theories, a new kind of infrared divergences emerges from loop integrals. While in ordinary 2-derivative theories in d=4 IR divergencies are associated with the emission of soft or collinear particles by almost on-shell external legs, in HD theories IR divergencies are also observed in far off-shell processes. For this reason, the usual procedure of reabsorbing IR effect in "dressed" IR-safe asymptotic states seems to fail in this case. These kinds of new IR enhancements have been treated in different ways during recent years, in particular within the context of quadratic gravity. We will discuss how these IR divergences are generated, showing in which way they are intrinsically different with respect to the well-known two derivative case. Then we will see how symmetries and some particular cancellations peculiar to higher derivative theories can help in defining well-defined scattering amplitudes.

Speaker: Diego Buccio (Heidelberg University)

95 Renormalization Group Approach to the Gravitational Two-Body Problem

The increasing precision of gravitational-wave observations demands analytical frameworks capable of accurately describing the relativistic dynamics of compact binaries beyond standard perturbation theory. While post-Newtonian and post-Minkowskian expansions have been highly successful, their intrinsically perturbative nature limits their applicability in strongly relativistic regimes.

In this talk, I present a formulation of the classical gravitational two-body problem based on Exact Renormalization Group (ERG) techniques. We construct classical analogues of the Polchinski and Wetterich flow equations and clarify their relation to standard perturbative expansions. In particular, we show how the ERG flow systematically reproduces the post-Newtonian expansion.

We also explore non-perturbative approximation schemes within the ERG framework for the conservative dynamics of binary systems. These results suggest that ERG methods offer a promising intermediate approach between perturbation theory and numerical relativity, with potential applications to precision gravitational-wave modeling.

Speaker: Facundo Gutierrez (Universidad de la Republica, Uruguay)

Parallel Session: Room 2

96 A complex LPA for the critical and multicritical Lee-Yang fixed points

The multicritical generalizations of the Lee-Yang universality class arise as RG fixed points of scalar field theories with complex $i\phi^{2n+1}$ interaction, just below their upper critical dimension. It has been recently conjectured that their continuation to two dimensions corresponds to the non-unitary conformal minimal models M(2,2n+3). Motivated by that, I will revisit the functional renormalization group approach to complex PT-symmetric scalar field theories in the Local Potential Approximation, aiming to explore the fate of the $i\phi^{2n+1}$ theories from their upper critical dimension to two dimensions. I will present how the conjecture is found consistent for n=1, while for n>1, how we are unable to follow the fixed points to d=2 due to their annihilations with unexpected non-perturbative fixed points at d>2. This is based on https://arxiv.org/abs/2601.15087

Speaker: Fanny Eustachon (École polytechnique)

97 Exploring Temperature-Resistant Order in Quantum Field Theories

It was recently established that spontaneous symmetry breaking (SSB) can persist at all temperatures in certain quantum field theories (QFTs) that involve two scalar fields. This construction is based on the existence of a suitable fixed point, promoting the QFT to a conformal field theory (CFT) and thereby ensuring that the theory is well-defined in the high-temperature limit. In my contribution, I will discuss recent advances in extending these theories to include Dirac fermions as well multiple scalar fields. I will show that the inclusion of these additional degrees of freedom does not lead to any new fully interacting CFTs that show SSB at finite temperature in three dimensions. Furthermore, I will present a construction including Dirac fermions that defines a class of QFTs that show spontaneous breaking of a spacetime symmetry above a critical temperature. If time permits, I will also discuss the possibility of extending these ideas to the Berezinskii-Kosterlitz-Thouless transition.

Speaker: Bilal Hawashin

98 Derivative Expansion, Frustrated Antiferromagnets and $O(N)\times O(2)$ models

We will present the “Derivative Expansion” as applied to the study of scalar models with $O(N)\times O(2)$ symmetry. These models describe Stacked Triangular Antiferromagnets, which have been the subject of a long-standing controversy regarding the order of the phase transition for the experimentally studied cases $N=2$ and $N=3$ in $d=3$. A brief review will be given of previous studies of these systems and recent advances in the use of the Derivative Expansion. It will be explained how these advances allow for the establishment of a small parameter in the calculation of long-distance properties of a wide variety of critical models. It will be explained why this is of interest not only in applications to statistical physics but also in many problems in quantum field theory. In the case of $O(N)\times O(2)$ symmetry, it allows us to establish with unprecedented accuracy that the transition for $d=3$ is first-order for both $N=2$ and $N=3$.

Speaker: Nicolás Wschebor (Instituto de Física de la Facultad de Ingeniería, Udelar (Uruguay))

99 Critical Phenomena on the Bethe Lattice

We investigate the critical behavior of a family of $\mathbb{Z}_2$-symmetric scalar field theories on the Bethe lattice (the tree limit of regular hyperbolic tessellations) using both the non-perturbative Functional Renormalization Group and lattice perturbation theory. The family is indexed by the parameter $\zeta \in (0,1]$, which determines the range of the theory via the kinetic term constructed from the graph Laplacian raised to the power $\zeta$. Specifically, $\zeta=1$ is the short-range theory, while $0<\zeta<1$ defines the long-range model. Due to the hyperbolic nature of Bethe lattices, the Laplacian lacks a zero mode and exhibits a spectral gap. We find that upon closing this spectral gap by a modification of the Laplacian, the scalar field theories exhibit novel critical behavior in the form of non-trivial fixed points with critical exponents governed by $\zeta$ and the spectral dimension $d_s=3$. In particular, our analysis indicates the presence of a Wilson-Fisher fixed point for the short range $\zeta =1$ theory. In contrast, the nearest‐neighbor Ising model on the Bethe lattice is known to exhibit mean‐field critical exponents. To the best of our knowledge, this work provides the first evidence that a scalar $\phi^4$ theory and the discrete Ising model on the same underlying lattice may lie in distinct universality classes.

Speaker: Saswato Sen (Okinawa Institute of Science and Technology)

Parallel Session: Room 3

100 Triviality doesn't mean Gaussianity: A Renormalization Group perspective

The Central Limit Theorem does not hold for strongly correlated stochastic variables, as is the case for statistical systems close to criticality. Recently for the three-dimensional Ising model, the calculation of the probability distribution function (PDF) of the total spin: $P(L^{-d}\int d^{d}x~\phi(x)=s)$ at criticality has been performed with the functional renormalization group. It has been shown that there exists an entire family of universal PDFs $P_{\zeta}(s)$ parameterized by $\zeta=\lim_{L,\xi_\infty\rightarrow\infty}L/\xi_\infty$ which is the ratio of the system size $L$ to the bulk correlation length $\xi_{\infty}$ with both $L,\xi_{\infty}\to\infty$. Using the $\epsilon=4-d$ expansion scheme in perturbation theory, we compute in three dimensions the whole family of $P_{\zeta}(s)$ up to two-loop order. I will finally show that in $d\geq 4$, even though the infrared-fluctuations are Gaussian--these universal PDFs are not, thereby showing why triviality doesn't mean Gaussianity.

Speaker: Sankarshan Sahu (LPTMC, Sorbonne Université)

101 SO (1, d+1) symmetry of the exact RG equation

There is a method for constructing from first principles, a holographic bulk dual action in Euclidean $AdS_{d+1}$ space for a $d$-dimensional Euclidean CFT on the boundary, starting from the Polchinski's Exact RG (ERG) equation that describes the RG evolution of the interaction part of the boundary Wilson action. The bulk action in $AdS_{d+1}$ has an $SO(1,d+1)$ symmetry and is obtained from the evolution operator of the Polchinski's ERG equation by a map that involves a field redefinition and requires a special form of the UV cutoff function in the ERG equation. In this paper, we show that for any form of the cutoff function, the ERG evolution operator has an $SO(1,d+1)$ symmetry. The generators of the special conformal transformation depend on the cutoff function. For the special cutoff function that maps to $AdS$ space, the transformations have the standard form of $AdS$ isometry. We also show that the ERG evolution operator for the full Wilson action can be put in the same form as the Polchinski's ERG equation by a field redefinition and consequently also has an $SO(1,d+1)$ symmetry for any cutoff function.

Speaker: Ms Semanti Dutta (S.N. Bose National Center for Basic Sciences)

102 Summation of logarithmic quantum corrections based on the locality of QFT

From the locality condition of quantum field theory and the Bogoliubov-Parasiuk-Hepp-Zimmerman procedure, we will derive universal expressions that allow summation of complete series of singularities and logarithms in quantum field theory. To demonstrate, we will apply this approach to an effective theory with arbitrary scalar potential, where we sum the leading and subleading logarithmic corrections.

Speaker: Alfiia Mukhaeva (Joint Institute for Nuclear Research)

103 Linearity in the renormalization group equations

As has recently been shown, the approach of summing logarithmic quantum corrections based on the locality of quantum field theory leads to sets of linear differential equations. Sometimes, obtaining such equations is a hard task. Since renormalizable quantum field theory has Callan-Symanzik renormalization group equation, we can apply a linearization procedure that allows us to determine these linear differential equations, which correspond to the summation of logarithms to the corresponding order of perturbation theory. This approach allows us to advance to higher orders of perturbation theory.

Speaker: Denis Tolkachev (Joint Institute for Nuclear Research)

12:20 Buffet Lunch

13:30 Confernce Excursion

Friday 4 September

104 Zonostrophic instability in beta-plane turbulence

We study a simplified model of geophysical flows, called beta-plane turbulence, which is built on the two-dimensional Navier-Stokes equation in the presence of differential rotation, ie a northward gradient of the local vertical rotation rate (beta-effect). When strong enough, the beta-effect triggers a zonostrophic instability, leading to the spontaneous emergence of zonal jets, which are large, banded, anisotropic alternating jets in the zonal direction. The complete theoretical description of the statistical properties of the jets and the related scaling regimes is still lacking. In this work, we use FRG to study the conditions for the zonostrophic instability, and we calculate the energy spectra associated with the jets and the background fluid.

Speaker: Léonie Canet (Université Grenoble Alpes)

105 Weak to strong wave turbulence: RG, large N, and epsilon expansion

The theory of wave turbulence -- developed over the past five decades -- is a consistent framework for describing cascades in a broad class of weakly interacting systems including: waves in the ocean, plasma waves, spin waves, acoustic waves, and many others. The Kolmogorov-Zakharov scaling for the distribution of mode occupation numbers is a solution of the weakly interacting kinetic equations, which been verified numerically and/or experimentally in a number of contexts. If the flux pumped into the system is large, or even if the flux is small and one is far along the cascade (at a wavenumber that differs significantly from the pumping scale) -- as is often the case in physical realizations -- the standard weak wave turbulence theory is insufficient.

We describe how this problem of find strong wave turbulence scaling can be mapped onto a problem of renormalization group flows in far-from-equilibrium states. Two contexts are solvable. The first is large N: We study turbulent cascade in a large N nonlinear Schrodinger equation. We find two forms of universality in the strong turbulence spectrum: in focusing media it is independent of the flux magnitude (the widely used critical balance solution), while in defocusing media it is independent of the bare coupling constant, with the largest scale appearing instead. These results are confirmed by direct numerical simulation. The second is the epsilon expansion. We conclude with a discussion of how FRG may be a useful tool for solving the problem of strong wave turbulence scaling in a general nonlinear system.

Speaker: Vladimir Rosenhaus

106 Universality Far from Equilibrium: New Fixed Points and New Challenges for RG

The renormalization group starts from an effective field theory -- but where does that theory come from? In hydrodynamics, the relevant degrees of freedom and symmetries can themselves emerge at long wavelengths. The Navier–Stokes equation provides a paradigmatic example: conservation laws and emergent symmetries strongly constrain the form of the long-wavelength theory, largely independently of microscopic details.

Far from equilibrium, this hydrodynamic viewpoint becomes particularly fertile. Unshackled by detailed balance, the space of allowed dynamical theories expands dramatically: new nonlinearities become possible, emergent symmetries can arise, and RG fixed points and universality classes (UCs) proliferate [1].

I will illustrate these ideas using active matter. I will first discuss the ordered phase of polar flocks [2–6], where emergent symmetries strongly constrain the RG flow and can lead to exact scaling relations. I will then turn to the critical behaviour of active Ising models, where nonequilibrium couplings generate a remarkably rich fixed-point structure, including a new UC that supersedes the equilibrium Wilson–Fisher UC as the generic description of the critical transition [7].

These examples highlight two complementary challenges for RG far from equilibrium: constructing the appropriate long-wavelength theory and tackling the proliferation of nonlinearities that arises once the constraints of equilibrium are lifted. I will conclude by asking whether functional RG approaches can help address the latter challenge.

[1] P. Jentsch and C. F. Lee, Hydrodynamics, Renormalization Group, and Universality Classes Far from Equilibrium, arXiv:2607.02318.
[2] L. Chen, C. F. Lee, and J. Toner, Mapping two-dimensional polar active fluids to two-dimensional soap and one-dimensional sandblasting, Nat. Commun. 7, 12215 (2016).
[3] L. Chen, C. F. Lee, and J. Toner, Incompressible polar active fluids in the moving phase in dimensions d > 2, New J. Phys. 20, 113035 (2018).
[4] L. Chen, C. F. Lee, and J. Toner, Moving, Reproducing, and Dying Beyond Flatland: Malthusian Flocks in Dimensions d > 2, Phys. Rev. Lett. 125, 098003 (2020).
[5] L. Chen, C. F. Lee, A. Maitra, and J. Toner, Dynamics of packed swarms: Time-displaced correlators of two-dimensional incompressible flocks, Phys. Rev. E 109, L012601 (2024).
[6] P. Jentsch and C. F. Lee, New Universality Class Describes Vicsek’s Flocking Phase in Physical Dimensions, Phys. Rev. Lett. 133, 128301 (2024).
[7] M. Wong and C. F. Lee, New Universality Classes Govern the Critical and Multicritical Behavior of an Active Ising Model, arXiv:2507.06068.

Speaker: Chiu Fan Lee (Imperial College London)

10:30 Coffee

107 Exact RG and generative diffusion model

In recent years, the rapid advancement of generative AI, particularly diffusion models, has led to the adoption of new data-driven methods in widely diverse fields—from high-quality image generation to drug discovery and material design. In this talk, I will discuss their theoretical similarities to the theory of the exact renormalization group widely used in statistical and high-energy physics. Specifically, I will introduce an approach based on RG concepts that aim to capture the hierarchical structure of data more efficiently.

Based on K. Masuki and YA, arXiv:2501.09064

Speaker: Yuto Ashida (The University of Tokyo)

108 The Hunting of Physics with Machine Learning through the (f)RG Looking Glass, and what we found there: An Agony, in two to eight Fits

In this talk I give a -certainly incomplete- overview of the rapidly growing area of

(i) physics and renormalisation group applications with Machine Learning

as well as

(ii) Machine Learning with the renormalisation group.

Applications (i) use the nonlinear optimisation property of neural networks for physics. Applications
(ii) use the fact that the layerwise or even global information transport in deep neural architectures is
either explicitly or implicitly a general (functional) renormalisation group transformation. Specifically, this
allows us to endow generative architectures which much-needed information beyond the learning sample.

Applications and ideas in (i,ii) are illustrated within simple examples.

Speaker: Jan M. Pawlowski

109 Non-Fermi-liquid metals and phase reconstruction: an FRG perspective

In this talk, I will briefly review the projects from my group’s work over the past decade or so in which the functional renormalisation group (FRG) has played a significant role. Most of these concern the theoretical description of non-Fermi-liquid metals (strongly interacting fermionic fluids without Landau quasiparticles), which often occur due to proximity to a quantum critical point. I shall present results on non-Fermi-liquids caused by proximity to a ferromagnetically ordered phase [1], proximity to a Pomeranchuk instability [2], and the presence of a gauge boson [3]. I shall also briefly present some recent results in which the numerical truncated-unity functional renormalisation group (TU-FRG) method is used to predict the phase reconstruction that occurs in the vicinity of a higher-order Van Hove point in the non-interacting band structure of the material [4].

[1] S. P. Ridgway and CAH, “Non-Fermi-Liquid Behavior and Anomalous Suppression of Landau Damping in Layered Metals Close to Ferromagnetism,” Phys. Rev. Lett. 114, 226404 (2015).
[2] M. J. Trott and CAH, “Non-Fermi-liquid fixed points and anomalous Landau damping in a quantum critical metal,” Phys. Rev. B 98, 201113(R) (2018).
[3] T. P. Sheerin and CAH, “Non-Fermi liquid induced by U(1) gauge-field interactions: A functional renormalization group analysis,” Phys. Rev. Research 7, 023216 (2025).
[4] T. P. Sheerin, M. Ramirez, CAH, and L. C. Rhodes, “Engineering correlated phases through manipulation of Van Hove singularities,” arXiv preprint 2608.07714 (2026).

Speaker: Chris Hooley (Coventry University)

12:30 Lunch

Parallel Session: Room 1

110 Scaling regimes of the 1D Kuramoto-Sivashinsky equation

The Kuramoto-Sivashinsky (KS) equation describes various phenomena that exhibit instabilities, such as flames and reaction-diffusion systems. It resembles another famous non-equilibrium stochastic model - the Kardar-Parisi-Zhang (KPZ) equation, the main difference being the negative "viscosity" in the KS equation.
It is known that the KS equation falls into the KPZ universality class, that is, at large length and time scales its statistical properties are those of the KPZ fixed point, with dynamical exponent $z=3/2$. At small scales and short times, another regime with $z=2$ was observed, which corresponds to the Edwards-Wilkinson UV fixed point of the KPZ equation.
In this work, we show, using FRG, that a third regime emerges at small scales and large times, which corresponds to the Inviscid Burgers fixed point of the KPZ equation with $z=1$ [1]. In the KPZ equation, this regime is observed if one tunes the bare viscosity to a very small value. In the KS equation, this regime is intrinsic and induced by the dynamics: the effective viscosity must cross zero when flowing from a negative bare value to a positive KPZ value at large scales.
Our analysis is based on the 2-point correlation function of the KS equation, that we calculate in a wide range of momenta and frequencies, which allows us to identify the regions where these three scaling regimes occur. This is done with the help of the "two grids" method, which was developed in the context of the KPZ equation [2].

[1] L. Gosteva, D. Roy, N. Wschebor, L. Canet, "Inviscid scaling in the Kuramoto-Sivashinsky equation from functional renormalization group and direct numerical simulations", to be submitted (2026).
[2] L. Gosteva, N. Wschebor, L. Canet, "Unveiling the different scaling regimes of the one-dimensional Kardar–Parisi–Zhang–Burgers equation using the functional renormalisation group", Journal of Statistical Mechanics: Theory and Experiment 2025, 114002 (2025).

Speaker: Liubov Gosteva (UGA)

111 Long range to short range crossover in one dimension

We study critical phenomena in one-dimensional systems with long-range (LR) interactions, with a focus on the crossover to short-range universality. Employing functional renormalization group calculations and large-scale Monte Carlo simulations of self-avoiding Lévy flights on a 1D lattice, we determine the anomalous dimension η, the correlation length exponent ν, and the susceptibility exponent γ over a broad range of the LR decay parameter σ. Our results provide strong numerical evidence in favor of Sak's scenario: we locate the crossover at σ* = 1 and show that critical exponents vary continuously across this point, while significant corrections to scaling are present.

Speaker: Tilman Enss (Heidelberg University)

112 Dynamical criticality beyond the overdamped limit

We develop a perturbative renormalization-group framework for dynamical critical theories that interpolates between overdamped and propagating dynamics. Although the formalism includes the purely dissipative Model-A limit as a special case, our main focus is the opposite regime, where dissipation is weak or absent and the dynamics is dominated by second-order time derivatives.

Within the supersymmetric MSRJD formulation, we compute the one- and two-loop contributions to the relevant vertex functions using dimensional regularization in (d=4-\epsilon), and derive the corresponding beta functions and anomalous dimensions. This allows us to determine the fixed-point structure and the associated critical exponents in the dissipationless regime, while keeping track of how the overdamped Model-A limit is recovered within the same formulation. The calculation therefore provides a controlled (\epsilon)-expansion approach to the crossover between dissipative and propagating critical dynamics.

Speaker: Dr Laura Batini

113 Wave interaction in astrophysical plasmas

Depsite being ubiquitous in the universe, plasmas still remain today a quite mysterious state of matter. Among the difficulties describing them is the fact that, even when they are dilute, the Coulomb interaction between electrons and ions is a long-range strong force.
In this talk, we show how the fRG tools can be used to get a better understanding of the interactions between structures at various scales within a simple model of a plasma.

Speaker: Olivier Coquand (LAMPS/University of Perpignan)

114 A Functional Renormalization Group Approach to Anomaly Detection via Dimensional Phase Transitions

Detecting signals within nearly continuous spectra remains a fundamental challenge in statistical inference, particularly in high-noise regimes where standard random matrix theory approaches, such as the Baik-Ben Arous-Péché (BBP) transition, frequently fail. We introduce a methodology that bridges statistical mechanics and statistical inference. By treating the empirical spectrum as an effective equilibrium field theory, we establish a formal mapping between anomaly detection and the Functional Renormalisation Group (FRG) flow of non-equilibrium systems using a stochastic field framework, wherein the noise-to-signal ratio functions mathematically as a physical temperature. Instead of treating signals as isolated statistical outliers, the FRG approach models them as ordered domains emerging within a thermalised background of fluctuations. This dynamic induces a structural deformation of the spectral geometry. By using the scale-dependent canonical dimension of this geometry as a highly sensitive order parameter, we demonstrate how the system undergoes a sharp dimensional phase transition. Expanding upon fundamental formulations, our results show that this transition directly correlates with stochastic ergodicity breaking, a spontaneous $\mathbb{Z}_2$ symmetry breaking in the effective potential, and a measurable deviation of eigenvector statistics from the universal Porter-Thomas distribution. Consequently, this enables signal resolution at signal-to-noise thresholds significantly below standard limits, even when the underlying data distribution closely follows the Marchenko-Pastur law. Furthermore, we validate the framework on realistic datasets, including those typical in computer vision, and critical phenomena, such as the determination of the phase transition temperature in physical systems. The FRG thus provides a rigorous, physics-grounded technique for extracting extensive-rank signals in complex datasets.

Speaker: Riccardo Finotello (CEA Paris-Saclay)

finotello_dft.pdf

Parallel Session: Room 2

115 Physics-informed neural networks for solving FRG

Although the formulation of the FRG is exact, practical calculations must be carried out approximately. This is because solvers for functional differential equations (FDEs), such as the Wetterich equation, have not yet been established. Meanwhile, physics-informed neural networks (PINNs) have recently gained attention as an efficient method for solving high-dimensional partial differential equations. Since FDEs are essentially high-dimensional differential equations, PINNs are expected to serve as useful solvers for the FRG. In this talk, I will discuss the application of PINNs to the FRG. In particular, I will present numerical applications to low-dimensional scalar models to demonstrate their applicability. In our approach, the effective action is represented by a neural network, and I will discuss network architectures that help ensure convexity, which is important for describing phase transitions. This talk is based on Refs. [1,2].
[1] T. Yokota, Physics-informed neural networks for solving functional renormalization group on a lattice, Phys. Rev. B 109, 214205 (2024).
[2] T. Miyagawa and T. Yokota, Physics-informed neural networks for functional differential equations: cylindrical approximation and its convergence guarantees, NeurIPS2024 (2024).

Speaker: Takeru Yokota

116 Solving Functional Renormalization Group Equations with Neural Networks

We employ deep neural networks to represent the field derivative of the scale-dependent effective potential in the functional renormalization group (fRG) framework for nonperturbative quantum field theory. By embedding the fRG flow equations directly into the loss function, the network parameters are determined so as to provide a continuous and differentiable representation of the scale- and field-dependent effective potential without relying on precomputed training data. Focusing on the O(N) scalar field theory within the local potential approximation at finite temperature, we demonstrate that this neural network representation accurately captures the renormalization group flow across symmetric, broken, and critical regimes. A key ingredient is a decomposition of the representation into an analytically known large-N contribution and a learned finite-N correction, which efficiently mitigates numerical stiffness associated with convexity restoration in the broken phase. The physics-driven solutions show excellent agreement with established finite-difference and discontinuous Galerkin methods. We further apply the same strategy to the Wilson-Fisher fixed point equation in three dimensions, illustrating that neural network representations provide a unified framework for both scale-dependent flows and fixed-point problems. Our results indicate that physics-driven deep learning offers a robust and flexible numerical tool for functional renormalization group studies.

Speaker: Yang-yang Tan

117 Existence theorem on the UV limit of Wilsonian RG flows

In Euclidean signature, we show that under mild conditions a nonterminating Wilsonian renormalization group (RG) flow of Feynman measures has a factorization property: there exists a regularization-independent ultimate Feynman measure (UV limit), from which the flow originates via pushforward (marginal) by the regulators. In addition, we prove certain existence theorems on the UV limit interaction potentials. We also show that whenever a (possibly effective) Wilsonian flow is described by a family of reference free Gaussian measures modified by a family of running interaction potentials, then the parameters of the reference Gaussian measure cannot run: a possible running mass or field renormalization factor must be present rather in the running potential. In arbitrary signature, an analogy of the measure existence theorem will be stated, for the Wilsonian RG flow of formal moments (correlators). Joint work with Zsigmond Tarcsay and Jobst Ziebell [Class.Quant.Grav.41(2024)125009 and J.Phys.A59(2026)035401].

Speaker: Andras Laszlo (HUN-REN Wigner Research Centre for Physics (HU))

erg2026laszlo.pdf

118 Flow equations of second order

Functional renormalization group flow equations can be constructed to be ultraviolet finite but break reflection positivity / unitarity, or vice versa. We explore how this problem can be circumvented with flow equations of second or higher order. They respect unitarity and are ultraviolet finite, but their solution leaves certain integration constants open. We discuss the physical significance of the latter. What emerges thus is a new functional RG scheme, that can be applied advantageously for addressing many questions concerning the dynamics of quantum field theories.

Speaker: Prof. Stefan Floerchinger (University of Jena)

119 Singularities in the RG flow

The conventional picture of the renormalization-group (RG) flow is that of a smooth evolution in coupling space, which becomes approximately linear in the vicinity of fixed points. In this framework, relevant and irrelevant directions are identified through the scaling properties of perturbations around the fixed point.

However, there are important physical situations in which the RG evolution develops singular behavior, leading to strongly accelerated and highly nonlinear flows. In this talk, I discuss two examples of such phenomena: spontaneous symmetry breaking and the formation of bound states. In both cases, the appearance of singular structures in the RG dynamics signals the breakdown of the standard perturbative scaling picture.

These examples suggest that relevance and renormalizability may not be determined solely by local power-law scaling near fixed points, but can also be shaped by global and singular features of the RG trajectory.

Speaker: Antal Jakovác (Wigner Research Centre for Physics)

Parallel Session: Room 3

120 Fermionic fRG with interaction flows : applications to electron-phonon systems

Conventional implementations of the functional renormalization group (fRG) rely on regulators for bare propagators only, notably in the framework of the Wetterich equation. Starting from Schwinger-Dyson and Bethe-Salpeter equations, we develop an fRG formulation where both bare propagators and bare interactions can be dressed with regulators. This makes the resulting fRG setup more flexible, allowing the implementation of approaches that are inaccessible to conventional fRG schemes. An example is the realization of temperature flows (which are commonly used to treat many-electron systems) for models with electron-phonon couplings.

In this talk, I will explain that this fRG formulation, based on regulators for bare interactions, is a generalization of the multiloop fRG, which has been shown to provide quantitatively accurate results for 2D lattice systems (beyond the conventional one-loop fRG derived from the Wetterich equation). The merits of a bosonization scheme called the single-boson exchange (SBE) decomposition will also be highlighted along the way. Finally, concrete applications will be presented for impurity models.

Speaker: Kilian Fraboulet

Presentation_ERG2026.pdf

121 Renormalisation group approaches for SU(N)xSU(M) symmetric Hubbard models

We develop a functional renormalization group (fRG) framework for two-dimensional Hubbard models whose fermions carry two independent flavor quantum numbers transforming under SU(N) and SU(M), respectively. Exploiting the product-group structure, we show that the two-particle vertex decomposes exactly into two independent scalar functions, reducing the one-loop flow to a closed system of equations for these flavor-singlet amplitudes.
We systematically compare parquet RG and truncated unity fRG calculations for SU(N)xSU(M) Hubbard models.

Speaker: Hannes Braun (Technische Universität München, Max Planck Institute for Solid State Research)

122 Functional renormalization group approach to boson-induced superconductivity in Bose-Fermi mixtures

In this talk I will discuss how the functional renormalization group (FRG) can be employed to study strongly interacting Bose-Fermi mixtures and, in particular, to predict and characterize mechanisms of boson-induced superconductivity. I will begin by reviewing how a self-consistent FRG framework captures the quantum phase transition from a polaronic condensate to a molecular Fermi gas observed experimentally in ultracold K-Rb mixtures [1], establishing the FRG as a reliable tool for strongly coupled Bose-Fermi systems where the interplay of competing scales precludes perturbative treatments. Building on this foundation, I will show how the strong-coupling physics of exciton-electron bound states — trions — gives rise to an emergent BCS-BEC crossover in doped atomically thin semiconductor heterostructures, where a renormalization group analysis demonstrates the relevance of beyond-Fröhlich interaction terms and predicts critical temperatures reaching up to 10% of the Fermi temperature [2]. Finally, I will present a self-consistent FRG approach to the problem of enhancing the critical temperature of an existing superconductor by coupling it to a thermal bosonic medium. Here, the mutual renormalization of fermion-fermion and boson-fermion vertices is essential: it predicts a robust enhancement of the superconducting temperature across a wide range of interactions, a nontrivial dependence on the boson mass, and a phase diagram featuring thermally induced, thermally enhanced, and BEC-induced superconductivity [3]. Throughout the talk I will emphasize how the FRG's ability to treat bosonic and fermionic fluctuations on equal footing provides physical insights that are inaccessible to conventional approaches.

References:
[1] M. Duda, X.-Y. Chen, A. Schindewolf, R. Bause, J. von Milczewski, R. Schmidt, I. Bloch, and X.-Y. Luo, Transition from a polaronic condensate to a degenerate Fermi gas of heteronuclear molecules, Nature Physics 19, 720 (2023).
[2] J. von Milczewski, X. Chen, A. Imamoglu, and R. Schmidt, Superconductivity induced by strong electron-exciton coupling in doped atomically thin semiconductor heterostructures, Phys. Rev. Lett. 133, 226903 (2024).
[3] E. Vlasiuk, M. Salmhofer, E. Demler, and R. Schmidt, Enhancing superconductivity using thermal bosons, arXiv:2603.06796 (2026).

Speaker: Richard Schmidt (Institute for Theoretical Physics, Heidelberg University, Germany)

123 Functional renormalization group for extremely correlated electrons

At strong on-site repulsion U, the fermionic Hubbard model realizes an extremely correlated electron system. In this regime, it is natural to derive the low-energy physics with the help of non-canonical operators acting on a projected Hilbert space without double occupancies. Using a strong-coupling functional renormalization group technique, we study the physics of such extreme correlations in the strict U = ∞ limit, where only kinematic interactions due to the Hilbert space projection remain. For nearest-neighbor hopping on a square lattice, we find that the electronic spectrum is significantly renormalized, with bandwidth and quasi-particle residue strongly decreasing with increasing electron density. On the other hand, damping and particle-hole asymmetry increase, while a polaronic continuum forms in the hole sector, below the single-particle band. Fermi liquid phenomenology applies only at low densities, where the system remains paramagnetic. At higher densities, we find a bad metal with strong magnetic correlations, indicating that the ground state is the Nagaoka ferromagnet at high densities and a stripe antiferromagnet at intermediate densities. Both in the paramagnetic and the ferromagnetic regimes, we observe a violation of Luttinger’s theorem.

Speaker: Andreas Rückriegel (Frankfurt University)

124 Control of ordered phases by manipulation of Van Hove singularities: insights from truncated-unity FRG

The engineering of exotic ordered states in two-dimensional itinerant electron systems is a matter central to the field of quantum materials, from the viewpoints of both fundamental physics and applications. Ordinary Van Hove singularities (VHSs), logarithmic divergences in the density of states arising from quadratic saddle points in a material’s dispersion, have long been known to induce strong correlations when situated at the Fermi level [1,2]; more recently, particular attention has been given to higher-order VHSs, whose power-law divergences (arising from higher-order saddle points in the dispersion) may further dramatically alter the adopted ordered state [3]. These strongly correlated phenomena are ideally studied using renormalization-group methods; however, such approaches have rarely been used to investigate how the phase diagram changes as the order of a VHS is tuned, or when the VHS is moved away from the Fermi level. Here, using the truncated-unity functional renormalization group (TUFRG), we perform an analysis of the square-lattice Hubbard model at weak coupling, in which varying a third-nearest-neighbour hopping ($t_3$) tunes the order of its VHSs. We also analyse the system using the parquet renormalization group in a patch scheme – comparing its results to those of TUFRG provides insights into the reliability of patch methods. We first pin the VHSs to the Fermi level and vary the hopping parameters, finding a rich landscape of phases that vary gradually but non-trivially with $t_3$. We then show that the system is much more sensitive to the energetic position of the VHSs, with some phases disappearing on perturbing very slightly from Van Hove filling. We conclude with some remarks on the implications our results have for the design of correlated two-dimensional materials.

References:
[1] A. Steppke, L. Zhao, M. E. Barber, T. Scaffidi, F. Jerzembeck, H. Rosner et al., Science 355, eaaf9398 (2017).
[2] G. Li, A. Luican, J. M. B. Lopes dos Santos, A. H. Castro Neto, A. Reina, J. Kong et al., Nature Phys. 6, 109 (2010).
[3] L. Classen and J. J. Betouras, Annu. Rev. Condens. Matter Phys. 16, 229 (2025).

Speaker: Dr Thomas Sheerin (University of St Andrews)

15:40 Coffee

125 Defect conformal field theories that are free in the bulk: A status report

Conformal field theories are relativistic quantum field theories with conformal symmetry. Defect CFTs have point or line or planar defects that further reduce the conformal symmetry to that of the defect. When the bulk is free and massless — a free massless scalar or fermion or photon — there are strong constraints on the conformal data that raise hope of achieving a partial or total classification of these theories. Moreover, some may have relevance for graphene, carbon nanotubes, and other experimental systems. We will survey recent results about these systems, including work in progress on free in the bulk fermions.

Speaker: Christopher Herzog

126 TBC

Speaker: Dr Enrico Pajer (University of Cambridge)

19:00 Conference Dinner

Saturday 5 September

127 Fermi scale from quantum gravity scaling solution

We propose that quantum gravity may predict the Fermi scale.
Fundamental scale invariance implies the scale invariant standard model.
Both the Fermi scale and the Planck mass are given by fields, and their ratio is dictated by a dimensionless cosmon-Higgs coupling.
For an ultraviolet fixed point of quantum gravity this coupling is an irrelevant parameter of the renormalization flow and becomes predictable. An analytic scaling solution for quantum gravity admits no free parameter for the mass term of the Higgs boson.
We discuss a new asymptotically safe quantum gravity fixed point for which the scalar potential is not flat.If the largest intrinsic mass scale generated by the renormalisation flow away from this fixed point is sufficiently below the Fermi scale, the couplings of the scale invariant standard model are determined by the scaling solution.
For a given short distance model remaining valid to infinitely small distances the ratio Fermi scale over Planck mass can then be predicted.
With reasonable assumptions for the ultraviolet fixed point a numerical solution finds a tiny value for the ratio between the Fermi and Planck scales, very close to a second order quantum electroweak phase transition. This could explain the observed gauge hierarchy.

Speaker: Christof Wetterich

FermiScaleQG.pdf

128 TBC

Speaker: Neil Turok (University of Edinburgh)

10:30 Coffee

129 Asymptotic behaviour of the derivative expansion in the ERG

We show that the derivative expansion of the exact (functional)
renormalization group is a divergent series in any dimension, both for an
exponential cutoff and more general smooth cutoffs. We prove this by showing
that within massless $\lambda\varphi^4$ perturbation theory, such divergences
arise first at two loops. From several lines of theoretical argument and by
analysing infinite classes of two- and three-loop contributions, we conclude
that the derivative expansion is an asymptotic series that initially converges
towards the exact result before divergent behaviour takes over.

Speaker: Prof. Tim Morris (University of Southampton)

130 Applications of the physics-informed renormalisation group

The resolution of strongly correlated systems is a computationally challenging task, which can be simplified enormously by choosing a formulation in terms of the appropriate degrees of freedom. Here, we distinguish between transformations of the fundamental degrees of freedom in the path integral, and transformations of mean fields.

Both are incorporated naturally in the renormalisation group approach and appear as dynamic, infinitesimal changes of the field representation with changing scales. A historically very prominent use case is dynamic rebosonisation, which implements the Hubbard-Stratonovich transformation throughout the RG flow, but recent investigations are studying a wider field of applications.

In my talk I will discuss the point of view of the physics-informed RG (PIRG) [1,2], which considers both the flow of a generating functional and the flow of the field on equal footing. This pair must fulfill a generalised flow equation and an additional constraint equation that can be chosen to suit a specific purpose.

Firstly, I we consider the PIRG for microscopic field-transformations [3]. Here, they bridge the gap to generative sampling architectures in lattice field theory. Specifically, the optimal transport nature of the RG allows to address long standing problems such as the sign-problem in real-time lattice simulations [4].
Secondly, I consider generalised flows of the effective action. Here the PIRG perspective allows to formulate novel optimisation procedures for expansion schemes [5,6], or the restoration of gauge symmetries which are explicitly broken by the RG flow [7,8]. 

[1] FI, J. M. Pawlowski, Annals Phys. 481 (2025) 170177
[2] FI, J. M. Pawlowski, Phys.Rev.D 113 (2026) 7, 076003
[3] FI, R. Kapust, J. M. Pawlowski, arXiv:2510.26678
[4] FI, R. Kapust, J. M. Pawlowski, arXiv:2603.03159
[5] FI, J. M. Pawlowski, arXiv:2305.00816
[6] A. Bonanno, FI, J. M. Pawlowski, SciPost Phys.Core 9 (2026) 005
[7] FI, J. M. Pawlowski, Phys.Rev.D 112 (2025) 10, 105005
[8] FI, B. Knorr, S. Mezger, J. M. Pawlowski, P. Sprenger, In preparation

Speaker: Friederike Ihssen (ITP Heidelberg)

131 Functional Renormalization and relativistic Luttinger fermions

We study the renormalization flow of relativistic Luttinger fermions as a new ingredient for the construction of UV-complete quantum field theories. The resulting fermion fields exhibit a canonical scaling different from Dirac fermions and thus support the construction of novel relativistic and perturbatively renormalizable, interacting quantum field theories in four spacetime dimensions. In particular, new asymptotically free self-interacting field theories can be identified, representing first examples of high-energy complete quantum field theories based on purely fermionic matter degrees of freedom. As examples, we discuss models which undergo dimensional transmutation and low-energy condensate formation with scalar excitations on top of the condensate. A corresponding Yukawa model exhibits features similar to self-organized criticality with a natural separation of low-energy observables from high energy initial scales without the need for any fine-tuning. We also critically examine the analytic structure of the Luttinger-fermionic propagator in the various gapped phases and discuss possible consequences for asymptotic states.

Speaker: Holger Gies (FSU Jena)

12:30 Lunch