# Equivariant Batalin-Vilkovisky formalism

## TL;DR

This paper develops an equivariant extension of the Batalin-Vilkovisky formalism for gauge theory quantization, addressing quantum master equation failures and applying it to supersymmetric Yang-Mills and Donaldson-Witten theories.

## Contribution

It introduces a general framework for equivariant BV formalism and applies it to extend AKSZ solutions, including examples in supersymmetric Yang-Mills and Donaldson-Witten theories.

## Key findings

- Recovered equivariant supersymmetric Yang-Mills in 2d
- Extended Donaldson-Witten theory within the formalism
- Provided a framework to handle quantum master equation failures

## Abstract

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 extension of AKSZ solutions of the classical master equation (CME). As examples of the construction, we recover the equivariant extension of supersymmetric Yang-Mills in 2d and of Donaldson-Witten theory.