Towards an FRG study of many-body localization

• Nicolas Dupuis

Disorder is known to induce a localized phase in a 1D Bose gas at zero temperature. It has been predicted that this insulating phase can survive at low temperatures, but the possible existence of such many-body localized phases in 1D quantum systems is a controversial issue. We discuss the finite-temperature phase diagram of a 1D disordered boson system using bosonization, the replica formalism and FRG. While the derivative expansion indicates that localization effects are still important at non-zero temperatures, it fails at low temperatures and we argue that a final answer regarding the existence of a true many-body localized phase can only be obtained from the BMW approximation.

Hydrodynamic attractors for strongly correlated fermions

• Tilman Enss

In heavy ion collisions, hydrodynamic attractors can describe out-of-equilibrium dynamics before hydrodynamics is expected to be valid. We describe how such behavior might be observed in real time in ultracold atomic Fermi gases. We present an efficient way to compute Green functions in real frequency beyond the derivative expansion and discuss how the system relaxes toward equilibrium. On relevant time scales, the dynamics is well represented by an analytical attractor solution that is valid at shorter times before the onset of Navier-Stokes hydrodynamics. The attractor represents an asymptotic series at long times and is complemented by nonhydrodynamic modes.

Central limit theorems, large deviations and the renormalization group

• Adam Rançon

The Ising model at criticality is a paradigmatic example of random variables displaying strong correlations at all scales. While in the high and low temperature phases the collective properties of the system are described by the standard (Gaussian) central limit theorem, the critical point separating the two phases is captured by a scale invariant and universal asymptotic probability distribution. From a physicist point of view, the emergence of such probability distribution is understood using the renormalization group, which effectively describes the behavior of coarse-grained random variables. In this talk, I will give a pedagogical overview of these concepts, using the probability distribution of the order parameter as an example of a non-trivial observable that can be computed using a functional version of the renormalization group. I will show that large deviations are universal, while very large deviation are non-universal. Furthermore, I will discuss how corrections-to-scaling can be rephrased in the langage of large deviations as a generalized Cramer's series.

Indications for particle physics from asymptotic safety

• Kamila Kowalska (National Centre for Nuclear Research)

There is growing theoretical evidence for the existence of an interactive UV fixed point in the renormalization group flow of the dimensionless couplings of the gravitational effective action. In the Standard Model and/or in models of New Physics embedded in the framework of trans-Planckian asymptotic safety, the presence of such a fixed point imposes Planck-scale boundary conditions on the gauge, Yukawa and scalar couplings. The ensuing fixed-point analysis often allows one to derive specific predictions for the IR phenomenology. Interestingly, it can also lead to the dynamical generation of arbitrarily small quantities, like for example the Yukawa couplings of Dirac neutrinos. In my talk I will review a set of phenomenological predictions obtained in recent years in the framework of trans-Planckian asymptotic safety and discuss possible experimental signatures of such scenarios.

Lorentzian Wetterich equations from the perturbative algebraic QFT perspective

• Kasia Rejzner

In this talk I will present recent results obtained in collaboration with d’Angelo, Drago and Pinamonti. We proposed a new formulation of renormalisation group flow equations that work on arbitrary globally hyperbolic spacetimes and for any chosen Hadamard state. The examples treated so far include the scalar field, Yang-Mills theories and gravity.

Finite formulation of QFT, naturalness, and the effective action

• Mikhail Shaposhnikov (EPFL - Ecole Polytechnique Federale Lausanne (CH))

I will provide an overview of the finite formulation of Quantum Field Theory (QFT) using the Callan-Symanzik method. This method enables the calculation of correlation functions without encountering intermediate divergences. I will discuss the impact of this technique on the hierarchy problem and naturalness, as well as its application to the quantum effective action in both renormalizable and non-renormalizable theories.

Renormalization of Effective Field Theories from Geometry

• Julie Pagès

The renormalization group equations (RGE) are a necessary component to comparing physics at different scales. For renormalized quantum field theories (QFT), there exists algebraic formulae, derived by ’t Hooft, which encode the one-loop counterterms of a wide class of theories. After reviewing how they were derived, we will extend to two-loop counterterms for scalar QFT. Moreover, we will see how these formulae can be applied to effective field theories (EFT) — theories with non-renormalizable higher-order operators — thanks to the geometric picture of EFT.

Asymptotic Safety and Vacuum Stability in the Litim-Sannino Model

• Tom Steudtner

I will review the progress in the Litim-Sannino model, where Asymptotic Safety occurs in a perturbatively controlled manner. Recent computations of three- and four-loop RGEs has opened new pathways to estimate the width of the UV conformal window. I will discuss the methods and phenomena constraining the window. In this regard, the stability of the scalar potential is an important observable. I will present how high-quality predictions are obtained from the quantum-improved potential.

Trace anomaly and renormalization group

• Omar Zanusso

I will review several aspects of the trace anomaly and its relation with the renormalization group.

Nonperturbative QCD within the functional renormalization group

• Wei-jie Fu (Dalian University of Technology)

In this talk, I would like to discuss recent progress in studies of nonperturbative QCD within the functional renormalization group (fRG) approach, focusing mainly on three aspects: QCD in vacuum and hadron structure, QCD at finite temperature and densities, and real-time dynamics of QCD. This concerns in more detail on the construction of fRG approach to first-principles QCD within the four-quark scatterings, and its application to the calculation of quasi-parton distribution amplitudes (PDA) for pions, QCD phase diagram and location of the critical end point (CEP), ripples of CEP, soft modes and the size of the static and dynamic critical region, the QCD moat regime, relaxation dynamics in QCD, etc.

Critical Dynamics and Non-Equilibrium Phase Transitions in QCD

• Lorenz von Smekal (Justus-Liebig University Giessen)

Some result of critical dynamics of the O(4) critical point in QCD

• Eduardo Grossi

Universal location of Yang-Lee edge singularity with Functional RG

• Vladimir Skokov

Low-energy effective theories of metals

• Sung-Sik Lee

The fixed points of the renormalization group flow are crucial for classifying phases of matter and understanding their universal low-energy physics. In metals, however, fixed points are defined only projectively due to the indefinite growth of Fermi momentum under scale transformations. In this talk, I will discuss the physical implications of the projective nature of metallic fixed points and the recent progress made in charting the space of universality classes for non-Fermi liquids.

UV complete field theory in (2+1)D with symmetry breaking at all temperatures

• Michael Scherer

It was recently established that spontaneous symmetry breaking can persist at all temperatures in certain biconical $\mathrm{O}(N)\times \mathbb{Z}_2$ vector models when the underlying field theories are asymptotically safe. So far, the existence of such models has only been explored in fractional dimensions for local but non-unitary models or in 2+1 dimensions but for non-local models. In my talk, I will discuss our study of local models at zero and finite temperature directly in 2+1 dimensions employing functional methods. At zero temperature, I show that our approach reproduces the critical behaviour with high accuracy for all $N\geq 2$. I will then exhibit the mechanism of discrete symmetry breaking from $\mathrm{O}(N)\times \mathbb{Z}_2\to \mathrm{O}(N)$ for increasing temperature near the biconical critical point when $N$ is finite but large. We calculated the corresponding full finite-temperature phase diagram and further showed that the Mermin-Wagner-Hohenberg theorem is respected within this approach, i.e., symmetry breaking only occurs in the $\mathbb{Z}_2$ sector. Finally, we also determined the critical value of $N$ above which this phenomenon occurs to be $N_c \approx 15$.

Symmetric improved estimators for multipoint vertex functions

• Jan von Delft

Multipoint vertex functions, and the four-point vertex in particular, are crucial ingredients in many-body theory. Recent years have seen significant algorithmic progress toward numerically computing their dependence on multiple frequency arguments. However, such computations remain challenging and are prone to suffer from numerical artifacts, especially in the real-frequency domain. Here, we derive estimators for multipoint vertices that are numerically more robust than those previously available. We show that the two central steps for extracting vertices from correlators, namely, the subtraction of disconnected contributions and the amputation of external legs, can be achieved accurately through repeated application of equations of motion, in a manner that is symmetric with respect to all frequency arguments and involves only fully renormalized objects. The symmetric estimators express the core part of the vertex and all asymptotic contributions through separate expressions that can be computed independently, without subtracting the large-frequency limits of various terms with different asymptotic behaviors. Our strategy is general and applies equally to the Matsubara formalism, the real-frequency zero-temperature formalism, and the Keldysh formalism. We demonstrate the advantages of the symmetric improved estimators by computing the Keldysh four-point vertex of the single-impurity Anderson model using the numerical renormalization group.

Different flavours of fermion quadrupling condensates in magic-angle twisted bilayer graphene

• Ilaria Maccari

Magic-Angle Twisted Bilayer Graphene is shown to host a large variety of interesting states of matter, including an unconventional superconducting state. 
But could this material form completely new states of matter? 

In this talk, I will discuss the possible emergence of two different types of electron condensates that go beyond the BCS coupling paradigm. These are condensates formed by fermionic quadruplets exhibiting no phase coherence between pairs of electrons, but between pairs of pairs. By employing large-scale Monte Carlo simulations on a low-energy effective model [1] for magic-angle twisted-bilayer graphene, we show that depending on the superconducting ground state, fermion quadrupling condensates may emerge as vestigial phases.

More specifically, we find that if the ground state is a superconductor additionally breaking time-reversal symmetry, a condensate formed by four electrons which breaks time-reversal symmetry generically emerges above the superconducting transition [2]. Conversely, if the ground state is a nematic superconductor, our numerical simulations show that the system exhibits a charge-4e phase before melting in the normal metal phase [3]. This indicates that twisted bilayer graphene is an ideal platform to stabilise and observe these novel quantum states. [1] D. V. Chichinadze, L.Classen, and A. V. Chubukov Phys. Rev. B 101, 224513 (2020); [2] I. Maccari, J. Carlström, E. Babaev, Phys. Rev. B 107 (6), 064501 (2023). [3] I. Maccari, J. Carlström, E. Babaev, In Preparation.

Diagrammatic approach to quantum spin systems

• Björn Sbierski

Frustrated quantum spin systems remain challenging to treat with state-of-the-art numerical methods. We review our recent fRG approach based on a pseudo-Majorana representation. We then turn to a rarely-applied diagrammatic formulation in terms of spin operators dating back to the 1960s. We pair this approach with modern computational capabilities and consider applications from the quantum optical community. We show that the resulting predictions for magnetic phase boundaries are surprisingly accurate. We also shed new light on a puzzling correspondence between spatial spin correlation patterns of quantum and classical spins where the latter are evaluated at a slightly elevated temperature.

Running couplings in quadratic gravity

• Roberto Percacci (SISSA)

One can define running couplings in various ways, some of which have a more immediate physical meaning. I will illustrate this in some scalar models and in quadratic gravity.

Gradient Flow Exact Renormalization Group

• Hidenori Sonoda

I am going to review a formulation of the exact renormalization group that reproduces gradient flows introduced earlier by Luescher. So far it has been successfully applied to QED. Applications to non-abelian gauge theories are for the future.

Asymptotic Safety Landscapes at the intersection between Positivity Bounds and Swampland Conjectures

• Alessia Platania

I will review recent progress in computing and analyzing the "landscape" of effective field theories stemming from an asymptotically safe ultraviolet completion of gravity. I will argue that this is an essential task in asymptotic safety, as well as in other approaches to quantum gravity, to test their consistency and to facilitate the comparison between their predictions. Concretely, I will focus on purely gravitational and gravity-photon systems, and I will discuss the intersections between the resulting asymptotic safety landscape, the string landscape identified by (some) swampland constraints, and positivity bounds.

O(3) Nonlinear Sigma Model and Non-Abelian Bosonization Duality

• Masatoshi Yamada

It is known that the SU(2) Wess-Zumino-Witten model is dual to the free fermion theory in two dimensions via non-Abelian bosonization. Additionally, the SU(2) Wess-Zumino-Witten model is believed to be equivalent to the O(3) nonlinear sigma model with the theta term. In this work, we reexamine this duality through the lens of renormalization group (RG) flow. We analyze the RG flow structure of the O(3) nonlinear sigma model with the theta term in two dimensions using the functional renormalization group. Our results reveal a nontrivial fixed point with a nonzero value of the topological coupling. The scaling dimensions (critical exponents) at this fixed point suggest the realization of duality between the O(3) nonlinear sigma model with the theta term and the free fermion theory, indicating that these models belong to the same universality class.

Living on the edge: Quantum black hole physics from the event horizon

• Francesco Sannino (University of South Denmark (DK))

In this talk, I will employ a particle physics approach to uncover universal insights into the quantum properties of black holes. This framework will enable us to calculate thermodynamic quantities of the black hole, including the Hawking temperature and entropy, using model-independent expressions. I will also deduce general consistency conditions for the metric deformations. The approach is relevant for several applications ranging from a deeper understanding of the nature of the space and time to (astro) particle physics and cosmology. Finally, I will also suggest a novel way of testing Hawking Radiation via Black Hole morsels observations by atmospheric Cherenkov telescopes, opening the way of testing new high energy physics scenarios before the advent of the next generation colliders.

When the RG must be functional and nonperturbative... Lessons from disordered systems

• Gilles Tarjus

40 years of Polchinski's equation

• Manfred Salmhofer