The gauging of BV algebras

TL;DR

This paper explores how to extend BV algebras to include gauging of global symmetries, leading to various gauge theories with different levels of ghostly supersymmetry and revealing new challenges in the framework.

Contribution

It develops a method for gauging global symmetries within BV algebras, including coupling to ghost systems with varying supersymmetry levels, and discusses emerging issues for higher symmetries.

Findings

Coupling to N=0 ghost system yields ordinary gauge theories.

Coupling to N=1 ghost system produces topological gauge theories.

Higher N ghost systems lead to complex topological theories with new problems.

Abstract

A BV algebra is a formal framework within which the BV quantization algorithm is implemented. In addition to the gauge symmetry, encoded in the BV master equation, the master action often exhibits further global symmetries, which may be in turn gauged. We show how to carry this out in a BV algebraic set up. Depending on the nature of the global symmetry, the gauging involves coupling to a pure ghost system with a varying amount of ghostly supersymmetry. Coupling to an N=0 ghost system yields an ordinary gauge theory whose observables are appropriately classified by the invariant BV cohomology. Coupling to an N=1 ghost system leads to a topological gauge field theory whose observables are classified by the equivariant BV cohomology. Coupling to higher $N$ ghost systems yields topological gauge field theories with higher topological symmetry. In the latter case, however, problems of a completely new kind emerge, which call for a revision of the standard BV algebraic framework.