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.
In quantum field theory, perturbative expansions of physical quantities such as propagators and
Green functions are generically asymptotic series with factorially divergent coefficients. This
obstruction prevents a direct determination of non-perturbative structure from perturbation theory
alone. In this talk, we investigate how resurgence theory provides a systematic framework to extract
non-perturbative information directly from perturbative data in the context of Schwinger–Dyson
equations [F. J. Dyson, The S Matrix in Quantum Electrodynamics, Phys. Rev. 75, 1736 (1949); J.
Schwinger, On the Green's Functions of Quantized Fields I & II, Proc. Nat. Acad. Sci. 37, 452–459
(1951)].
Starting from the Renormalization Group Equation governing the propagator in the massless
Wess–Zumino model, we perform a Borel transform to pass into the Borel plane, where the
divergent perturbative series becomes an analytic function with isolated singularities at integer
values of β0ξ. These singularities obstruct analytic continuation and are shown to encode
non-perturbative contributions to the physical propagator [M. Bellon, Schwinger–Dyson equations
and resurgence, (2017)].
Using the framework of resurgence introduced by Écalle [J. Écalle, Les Fonctions Résurgentes,
Publ. Math. d'Orsay, Vols. I–III (1981)], we define alien derivatives and the Stokes automorphism to
systematically characterize the monodromy structure around each singularity. The various
non-perturbative sectors — each associated with a transseries expansion around a distinct
singularity — are not independent, but are interrelated through the action of alien calculus, revealing
that the full non-perturbative structure of the theory is already latent within its perturbative
expansion.
