Related papers: Consistent deformations in the presymplectic BV-AK…
Using technique of wheeled props we establish a correspondence between the homotopy theory of unimodular Lie 1-bialgebras and the famous Batalin-Vilkovisky formalism. Solutions of the so called quantum master equation satisfying certain…
We review and extend the Alexandrov-Kontsevich-Schwarz-Zaboronsky construction of solutions of the Batalin-Vilkovisky classical master equation. In particular, we study the case of sigma models on manifolds with boundary. We show that a…
We consider the Wilson-Polchinski exact renormalization group applied to the generating functional of single-trace operators at a free-fixed point in $d=2+1$ dimensions. By exploiting the rich symmetry structure of free field theory, we…
We study the problem of consistent interactions for spin-3 gauge fields in flat spacetime of arbitrary dimension n>3. Under the sole assumptions of Poincar\'e and parity invariance, local and perturbative deformation of the free theory, we…
Topological gauge theories describe the low-energy properties of certain strongly correlated quantum systems through effective weakly interacting models. A prime example is the Chern-Simons theory of fractional quantum Hall states, where…
We study an equivariant extension of the Batalin-Vilkovisky formalism for quantizing gauge theories. Namely, we introduce a general framework to encompass failures of the quantum master equation, and we apply it to the natural equivariant…
We propose a program for bridging the gap between the perturbative BV-BFV quantization of Chern-Simons theory and the non-perturbative Reshetikhin-Turaev (RT) invariants of 3-manifolds, passing through factorization homology of…
The local cohomology of an extended BRST differential which includes global N=1 supersymmetry and Poincare transformations is completely and explicitly computed in four-dimensional supersymmetric gauge theories with super-Yang-Mills…
The purpose of this paper is to establish an explicit correspondence between various geometric structures on a vector bundle with some well-known algebraic structures such as Gerstenhaber algebras and BV-algebras. Some applications are…
Consistent boundary conditions for Alexandrov-Kontsevich-Schwartz-Zaboronsky (AKSZ) sigma models and the corresponding boundary theories are analyzed. As their mathematical structures, we introduce a generalization of differential graded…
We analyse completely the BRST cohomology on local functionals for two dimensional sigma models coupled to abelian world sheet gauge fields, including effective bosonic D-string models described by Born-Infeld actions. In particular we…
We prove that a sum of free non-covariant duality-symmetric actions does not allow consistent, continuous and local self-interactions that deform the gauge transformations. For instance, non-Abelian deformations are not allowed, even in 4…
In this article, we use the language of $\mathbb{P}_0$-factorization algebras to articulate a classical bulk-boundary correspondence between 1) the observables of a Poisson Batalin-Vilkovisky (BV) theory on a manifold $N$ and 2) the…
We give an example of how conventional gauging methods obstruct a systematic analysis of gauged supergravities. We discuss how the embedding tensor formalism deals with these problems and argue that the gauge algebra related to the…
Dijkgraaf-Witten (DW) theories are of recent interest to the condensed matter community, in part because they represent topological phases of matter, but also because they characterize the response theory of certain symmetry protected…
Yang-Mills gauge theory on Minkowski space supports a Batalin-Vilkovisky-infinity algebra structure, all whose operations are local. To make this work, the axioms for a BV-infinity algebra are deformed by a quadratic element, here the…
The Batalin-Vilkovisky master equations, both classical and quantum, are precisely the integrability equations for deformations of algebras and differential algebras respectively. This is not a coincidence; the Batalin-Vilkovisky approach…
Three dimensional topological field theories associated with the three dimensional version of Abelian and non-Abelian Seiberg-Witten monopoles are presented. These three dimensional monopole equations are obtained by a dimensional reduction…
Interrelations between discrete deformations of the structure constants for associative algebras and discrete integrable systems are reviewed. A theory of deformations for associative algebras is presented. Closed left ideal generated by…
We show that the de Rham complex of any almost Hermitian manifold carries a natural commutative $BV_\infty$-algebra structure satisfying the degeneration property. In the almost K\"ahler case, this recovers Koszul's BV-algebra, defined for…