Towards equivariant Yang-Mills theory

TL;DR

This paper develops an equivariant extension of the BV formalism for four-dimensional Yang-Mills theories, introducing non-local homological tools and extending the BV action to satisfy the equivariant master equation.

Contribution

It presents a novel equivariant BV framework for Yang-Mills theories, including explicit partial integration and a non-local extension of the BV action.

Findings

Derived a non-local homological generalization of Cartan calculus.

Extended the abelian YM BV action to satisfy the equivariant master equation.

Performed explicit BV push-forward in the abelian case.

Abstract

We study four dimensional gauge theories in the context of an equivariant extension of the Batalin-Vilkovisky (BV) formalism. We discuss the embedding of BV Yang-Mills (YM) theory into a larger BV theory and their relation. Partial integration in the equivariant BV setting (BV push-forward map) is performed explicitly for the abelian case. As result, we obtain a non-local homological generalization of the Cartan calculus and a non-local extension of the abelian YM BV action which satisfies the equivariant master equation.