Categorical Quantum computation, Fyodor Amanov (New Uszbekistan University)
On observables in 4D topological gauge-affine gravity, Oussama Abdelghafour Belarbi (Université Oran 1 Ahmed Ben Bella )
Using the BRST superspace formalism we arrive at a set of BRST symmetry (and anti-BRST symmetry) for a topological version of a gauge model of gravity based on gauging the general affine group. Moreover, a complete set of observables for a 4D topological gauge-affine gravity is obtained by means of the formalism of descent equations.
Chern-Simons-Like Formulation of Exotic Massive 3D Gravity Model, Büşra dedeoğlu (METU)
We investigate the Chern-Simons-like formulation of exotic general massive gravity models within the framework of third-way to three-dimensional gravity. We classify our construction into two main approaches: one using torsional cosmological Einstein and exotic massive gravity equations, and the other a torsion-free approach. The for mer approach, while mathematically appealing, precludes the construction of critical exotic models where the central charges vanish. In contrast, the latter approach has a wider parameter space and allows for the construction of critical models. An ex plicit example of an exotic general model is provided to illustrate both methods. Our methodology represents the first step towards establishing the most general Chern Simons-like formulation of third-way to three-dimensional gravity, which would enable the study of identifying its bulk/boundary unitary sector.
BV description of N=1, D=4 Supegravity and the Reduced Phase Space, Filippo Fila-Robattino (UZH)
The BV formalism was first introduced to deal with the perturbative quantization of gauge theories, generalizing the BRST procedure. It is well known that in the case of supergravity the supersymmetry transformations close only on-shell, leading to a rank-2 (i.e. quadratic in the antifields) BV action. In this work, we present a fully covariant BV description of N=1, D=4 supergravity in the first order formalism, allowing the spin connection to be dynamical. Assuming the space-time manifold admits a boundary, such choice provides the natural framework to study the reduced phase (RPS) space of the theory, which is given as the reduction of a coisotropic submanifold, hence admitting a cohomological description via the BFV formalism. However, such construction does not provide a BV/BFV extendible theory.
Spectrum of kinky vortices, Kunal Gupta (Uppsala University)
We study the spectrum of a special type of vortices in abelian Chern-Simons theory on a cylinder, called kinky vortices. We observe and conjecture a relationship between the CFIV indices of such vortices and open Gromov-Witten invariants of a toric Calabi-Yau threefold. This matching further allows us to go from knots to quivers within the knots-quivers correspondence, with the exact details reserved for a future paper.
Relative Trace Formulas in Geometry and Physics, Arne Hofmann (Leibniz University Hannover)
Relative trace formulas are related to the Casimir effect, a thriving area in theoretical and experimental physics. They are also related to wave-trace invariants in spectral geometry. This poster presents recent progress on relative trace formulas for different boundary conditions. This includes the case of transmission boundary conditions, which are important in order to understand the Casimir effect in realistic materials.
N=1 Supergravity to All Orders in Fermions, Julian Kupka (University of Hertfordshire)
We show that generalized geometry provides a natural and elegant formulation of N=1 supergravity in D=10 that extends to higher-fermion terms in both the action and supersymmetry transformations.
Dold-Kan type theorems, Daniil Kuzakov (Saint Petersburg State University)
A. Dold and D. Kan independently proved in 1958 that the category of simplicial abelian groups is equivalent to the category of chain complexes. Clemens Berger recently noticed that this phenomena has categorical interpretation: simplex category $\Delta$ has some families of ordered projectors. We try to explain it and apply to another categories.
Coherent sheaves on maximally singular algebraic varieties, Aleksei Lvov (Saint Petersburg State University)
We define and study the category $Coh(C_X)$ associated with an algebraic variety $X$. The category $Coh(C_X)$ is an inductive 2-limit of categories of coherent sheaves on singular models of $X$. It can be thought of as a category of coherent sheaves on a maximally singular model of $X$. We study some properties of this categories and prove that for a curve $X$ the global homological dimension of $Coh(C_X)$ is equal to 1.
Two-loop Schramm-Loewner evolution and CFT partition functions, Sid Maibach (Uni Bonn)
We study a generalization of the Schramm–Loewner evolution (SLE) loop measure to pairs of non-intersecting Jordan curves on the Riemann sphere. Addressing the question of minimization of the associated two-loop Loewner potential, we find that any such minimizers must be pairs of circles. However, the potential is not bounded, diverging to negative infinity as the circles move away from each other. To remedy the divergence, we study a way of generalizing the two-loop Loewner potential by taking into account how conformal field theory (CFT) partition functions depend on the modulus of the annulus between the loops. This generalization is motivated by the correspondence between SLE and CFT, and it also emerges from the geometry of the real determinant line bundle as introduced by Kontsevich and Suhov.
Asymptotic symmetries of gravity in the gauge PDE approach, Mikhail Markov (University of Mons)
This presentation, based on joint work with Maxim Grigoriev (arXiv:2310.09637), introduces a framework for studying local gauge theories on manifolds with boundaries and their asymptotic symmetries by representing them as so-called gauge PDEs. Gauge PDE approach generalizes conventional BV-AKSZ sigma-models to include systems that are not necessarily topological or diffeomorphism-invariant, and it remains well-defined when restricted to submanifolds and boundaries. We introduce the notion of gauge PDEs with boundaries, which accommodates generic boundary conditions, and apply this framework to asymptotically flat gravity. Starting from a suitable representation of gravity as a gauge PDE with boundary, aligned with Penrose’s description of asymptotically simple spacetimes, we derive the minimal model induced on the boundary, yielding a Cartan (frame-like) description of a conformal Carollian structure. Imposing an adapted version of standard boundary conditions within this model directly reproduces the conventional BMS algebra of asymptotic symmetries.
All 4 × 4 solutions of the quantum Yang–Baxter equation, Vera Posch (Trinity College Dublin)
In this work we complete the classification of 4 × 4 solutions of the Yang–Baxter equation. Regular solutions were recently classified and in this paper we find the remaining non-regular solutions. We present several new solutions. We then consider regular and non-regular Lax operators and study their relation to the quantum Yang–Baxter equation. We show that for regular solutions there is a correspondence, which is lost in the non-regular case. In particular, we find non-regular Lax operators whose R-matrix from the fundamental commutation relations is regular but does not satisfy the Yang-Baxter equation. These R-matrices satisfy a modified Yang–Baxter equation instead.
Renormalization of Gauge Theories and Gravity, David Prinz (MPIM)
The renormalization of gauge theories and, eventually, gravity is one of the biggest current challenges in mathematical physics. In this poster, I will describe recent progress in the Hopf algebraic approach to renormalization. Specifically, this amounts to the following two aspects: 1) Avoiding gauge and diffeomorphism anomalies, which translates to the validity of the corresponding Slavnov--Taylor identities: A theorem by van Suijlekom (2007), improved by myself (2022), states that they generate Hopf ideals. 2) Transversality of the formal Green's function, which can be implemented combinatorially via cancellation identities: In an ongoing project, I aim to implement these via a Feynman graph complex, similar to the one constructed by Kreimer et al. (2013). Specifically, I aim to relate both aspects in said project by extending the renormalization Hopf algebra to a differential-graded renormalization Hopf module, as outlined in my doctoral thesis, cf. arXiv:2210.17510 [hep-th]. Finally, I will address the application of these constructions to Quantum General Relativity, which is non-renormalizable by power counting: To overcome this issue, I will close with a recent working conjecture of mine for the appropriate UV-completion thereof.
Dressing and screening in Anti de Sitter Scalar QED, Veronica Sacchi (EPFL)
