Opening Room: A348

Laurent Baulieu Room: A348 **The Forgotten BRST Noether Current Ward Identity: 1.5 Noether Theorem for a Deeper Understanding of the Holography Principle in Asymptotically Flat Spaces**

Marc Henneaux Room: A348 **BRST Quantization of Constrained Hamiltonian Systems : the example of asymptotically flat gravity** Abstract: The BRST Quantization of Constrained Hamiltonian Systems is reviewed in the explicit case of gravity. The BRST reformulation of the Wheeler-DeWitt equation is discussed. Two specific questions are explicitly analyzed : (i) how to compute physical amplitudes between physical states ; (ii) how asymptotic symmetries appear in the BRST context (with special emphasis on the BMS group).

Claudia Scheimbauer Room: A348 **Is quantization functorial?** The axiomatic approach to (extended) topological field theories due to Atiyah-Segal-Lurie has been well-studied in the past decades. However, it still is unclear how to describe (BV) quantization in this framework. I will discuss what is known and what could be in the next 50 years.

Gong Show Room: A348 **Eugenia Boffo: BCOV reloaded** We inspect BCOV theory, a field theory for the deformations of complex structures that also maintain the new volume form still holomorphic. We show that the fields are the observables obtained by BRST quantization of a new topological particle model with (2;2) supersymmetry. Our most important achievement is the formulation of an action functional with the expected gauge symmetries, for both the relevant fields (Beltrami differential and scalar compensator). This is presented in the Batalin--Vilkovisky framework. We build on previous works [Barannikov-Kontsevich] in the theory of "potentials", i.e. primitives, w.r.t. the divergence operator. The non-invertibility of the Poisson structure ([BCOV] and [Costello-Li]) is still featured in our solution. **Thomas Basile: Multisymplectic AKSZ sigma models** Abstract: The Alexandrov–Kontsevich–Schwarz–Zaboronsky (AKSZ) construction encodes topological sigma models in terms of a symplectic Q-manifold. The beauty and efficiency of this construction is that it allows one to produce a solution of the classical master equation, with all the structures used in the BV formalism (e.g. introduction of ghosts and antifields, symplectic structure / BV bracket, etc) appearing directly from structures in the target space. Replacing the symplectic structure with a presymplectic one extends the framework to non-topological models and yields gauge-invariant actions providing a covariant multidimensional analogue of the first-order Hamiltonian action. We show that this construction admits a natural generalisation in which the target Q-manifold carries a differential form of arbitrary (possibly inhomogeneous) degree that is closed under d+L_Q​. This data defines higher-derivative generalisations of AKSZ actions that remain gauge invariant and admit a concise formulation via the Chern–Weil map of Kotov and Strobl. Several gauge theories, including higher-dimensional Chern–Simons theory, the MacDowell–Mansouri–Stelle–West action, and self-dual gravity with its higher-spin extensions, fit naturally into this framework. Based on [2601.16785] with Maxim Grigoriev and Evgeny Skvortsov. **Lennart Obster:** We will discuss a new point of view of representation theory of Lie groupoids and algebroids: fat Lie theory. We introduce the category of fat extensions (of groupoids), which is equivalent to the category of vector bundle groupoids, general linear principal bundle groupoids, and 2-term representations up to homotopy (which we introduce abstractly). We also mention core extensions, which are objects intimately related to fat extensions. Such objects correspond to vertically/horizontally core-transitive double groupoids and, therefore, regular fat extensions also correspond to general linear double groupoids. **Davide Rovere:** I present a brief summary of this work 2508.14591, with F. Fecit, where BV formalism for covariant fracton gauge theories is studied and some worldline model, BRST- quantised, are found. **Giovanni Mocellin: On a Categorical Approach to BV** The category of smooth sets, introduced by Sati and Giotopoulos in 2312.16301, is the category of sheaves over the site of Cartesian spaces with respect to the differentiably-good open covers. It naturally encodes many classical Bosonic Lagrangian field-theoretical constructions, and, in particular, the Cartan calculus on the field space when restricted to well-behaved de Rham forms and vectors. I will define the category of super thickened smooth sets, obtained by enlarging the site with an infinitesimal and super structure, and hint at how this could provide a categorical approach to the BV framework. **Julian Kupka: BV Theory of N = 1, D = 10 Supergravity** **Edwyn Tecedor: Resurgence analysis in the Ward-Schwinger-Dyson equation.**

Informal gathering with Brezen Room: A348

Alberto Cattaneo Room: A348 **Surface observables in 4D BF and Yang–Mills theories** Abelian Yang–Mills theory possesses an interesting gauge-invariant observable defined as (the exponential of) the Hodge dual of the curvature integrated on a surface Sigma (this can be interpreted as the magnetic flux through Sigma). As emphasized by ’t Hooft, a nonabelian version would be of significant interest. In this talk, I will first show how to obtain a surface observable for BF theory with cosmological constant. This is a topological field theory, and an AKSZ model, whose fields are a connection and a 2-form B, with equations of motions simply stating that B is proportional, by the “cosmological constant,”to the curvature. This is a nontrivial task which can be achieved through the BV formalism defining a second field theory on Sigma coupled to the ambient fields of BF theory. (As the previously known version for zero cosmological constant, the expectation value of this observable should yield invariants of 2-knots in 4 dimensions.) Subsequently, thanks to a result with F. Bonechi and M. Zabzine, we can recover Yang–Mills theory (plus quantum corrections) from this BF theory via averaging on certain fields (BV pushforward in the terminology developed with P. Mnev and N. Reshetikhin). This procedure also produces a surface observable for Yang–Mills theory which, in the classical limit, corresponds to the nonabelian magnetic flux.

Ezra Getzler Room: A348 **Cyclic L-infinity algebras and shifted symplectic forms** Abstract: Cyclic differential graded Lie algebras and their generalization, cyclic L-infinity algebras, are important in the study of quantum field theories. Kontsevich interpreted them as symplectic formal derived stacks. We explain how this perspective clarifies homological perturbation theory, which may be interpreted as a flow on the derived stack. Using a formal analogue of Cartan calculus, we extend homological perturbation theory to cyclic L-infinity algebras

Pavel Mnëv Room: A348 **Contribution of non-acyclic flat connections in Chern-Simons theory and invariants of 3-manifolds** Abstract: Path integral of Chern-Simons theory on a closed 3-manifold gives a family of perturbative partition functions (effective BV actions induced on twisted de Rham cohomology) parametrized by the moduli space of flat connections. This family is horizontal with respect to the Grothendieck connection modulo a BV-exact term. I will outline how (a) This family can be extended to a nonhomogeneous form over triples (kinetic flat connection, gauge-fixing flat connection, metric), satisfying a differential quantum master equation (i.e., is annihilated by an appropriate “Gauss-Manin” flat superconnection); (b) One can extract from the extended partition function above a volume form on the smooth irreducible stratum of moduli space, whose cohomology class is metric-independent, and hence yields an invariant of a framed 3-manifold. The talk is based on a joint work with Konstantin Wernli, arXiv:2510.18653, arxiv:2512.17638.

Domenico Fiorenza Room: A348 **BV algebras, they don't really exist** Given a differential graded Gerstenhaber algebra $(\mathcal{G},d,\cdot,\{,\})$ and a bigraded homotopy Cartan calculus for it, the choice of a Poincaré duality element enhances the Gerstenhaber algebra structure on $H(\mathcal{G})$ to a BV-algebra structure. Every BV algebra can be realized, essentially in a tautological way, as an instance of homotopy Cartan calculus with Poincaré duality. Possibly more interestingly, the dependence of the BV-laplacian on the choice of the Poincaré duality element provides a justification for the typically observed phenomenon that the BV-bracket is "more canonical" than the BV-laplacian. Classical examples of BV-algebras from homotopy Cartan calculus with Poincaré duality include the divergence of multivector fields on Riemannian manifolds and the Ginzburg-Menichi BV algebra structure on Hochschild cohomology. Possibly less known is the fact that Ševera's derivation of the BV-algebra structure on the Gerstenhaber algebra of functions on an odd symplectic manifold is an instance of homotopy Cartan calculus. No surprise, Poincaré duality elements in this setting are precisely compatible half-densities. Joint work with Eugenia Boffo.

Lionel Mason Room: A348 **Ambitwistor-strings, BRST and the Penrose transform** Abstract: Ambitwistor strings are chiral sigma models whose targets are spaces of complex null geodesics in complexified space-times. Their correlation functions generate remarkable formulae for complete tree-level S-matrices of a variety of massless theories including gauge and gravity theories. This talk will focus on the geometry of the correspondences. It will exaplain how BRST descent implements the Penrose transform that encodes space-time fields into cohomology classes on ambitwistor space and how quantum consistency encodes the nonlinear field equations of gauge and gravity theories.

Fridrich Valach Room: A348 **On type I supergravity and its twist** Abstract: We review the recent BV formulation of type I supergravity in 10 dimensions and then conjecture a description of its general twist in the sense of Costello and Li. In the special case of a Calabi-Yau 5-fold this recovers the conjectural relation between the twist and the associated Kodaira-Spencer theory.

Tudor Dimofte Room: A348 **BV-BRST for operator algebras** Abstract: I'll discuss BV-BRST formalism as a useful tool for analyzing algebras of local and extended operators, in topological and/or holomorphic field theories. I'll focus on examples from recent work, including A-infinity/chiral structures on local operators in 3d holomorphic-topological (HT) theories, line operators in 4d HT theories, and cohomological Hall algebras of BPS states.

Pavol Ševera Room: A348 **"Everything" is a boundary condition of AKSZ models** The chiral WZW model can be seen as the chiral boundary condition of the Chern-Simons theory. If we move from Chern-Simons to arbitrary AKSZ models, similar boundary conditions give us BV descriptions of "any" (possibly higher gauge) models whose fields are suitable differential forms. The simplest examples come from exact Courant algebroids, where the corresponding models will be (possibly gauged) 2d sigma models, and from Poisson sigma model, giving us Hamiltonian mechanics on the Poisson manifold (or on its reduction). Based on a joint work with Jan Pulmann and Fridrich Valach.

Si Li Room: A348 **Quantum BRST-BV in Topological/Holomorphic Theories** Abstract: We explain the ultra-violet finiteness property of topological/holomorphic theories, which leads to local equations of the corresponding quantum BRST-BV quantization.

Ingmar Saberi Room: A348 **Non-holonomic G-structures and supersymmetric field theories** The groundbreaking work of Becchi-Rouet-Stora and Tyutin marks the beginning of (or is at least a synecdoche for) the application of techniques from homological algebra to field theories. Such ideas have flourished over the intervening fifty years, encompassing not only gauge symmetry, but also the dynamics of Lagrangian field theories (after Batalin and Vilkovisky) and the theory of anomalies. I will discuss some modern developments of this line of ideas in the context of supersymmetric field theory.

Giovanni Canepa Room: A348 **BV Pushforward and Palatini-Cartan gravity** Abstract: In this talk I will show how to use a BV pushforward to correct some issues arising in the BV formulation of Palatini Cartan gravity. In particular, I will show that the standard BV formulation of gravity in the Palatini-Cartan formalism is equivalent to an AKSZ-like version compatible with BFV data on the boundary. This talk is based on arXiv:2507.06279, a joint work with A. S. Cattaneo.

Camillo Imbimbo Room: A348 **Beyond Chern-Simons: The Algebraic Topology of Superconformal Anomalies** Abstract: We present a unified BRST-cohomological framework for anomalies, extending the Chern-Simons formulation of Yang–Mills anomalies to encompass all four-dimensional superconformal anomalies. Central to our approach is the characterization of anomalies through the constraint ideal in the polynomial ring formed from generalized curvatures and connections of the underlying symmetry (super)-Lie algebra. In Yang–Mills theory, the constraint ideal is generated solely by curvatures, so anomalies correspond to invariant Chern curvature polynomials. In contrast, the constraint ideal for four-dimensional (super)conformal gravity includes additional polynomials that mix curvatures and connections. This enriched structure naturally explains the coexistence of both Chern-type (a) and non-Chern-type (c) anomalies in (super)conformal theories.

Maxim Zabzine Room: A348 **The equivariant B-model** Abstract: I will review the equivariant versions of A and B models and present some simple calculations. In the second part of the talk I will concentrate on equivariant B-model and outline some challenges in our understanding.

Francesco Bonechi Room: A348 **A BV approach to double copy**. Color kinematics duality is a feature of gauge theories that appears in the computation of physical amplitudes. Its most relevant application is the construction of the double copy theory. We discuss the underlying algebraic structure from the point of view of Batalin-Vilkovisky in the simplified (but meaningful) case of the off shell duality that was highlighted first for Chern-Simons. Time permitting, we also discuss the gravitational interpretation of the double copy. This talk is based on joint work with M.Ben Shahar and M. Zabzine.