Background gauge invariance in the antifield formalism for theories with open gauge algebras

TL;DR

The paper demonstrates that BRST invariant quantum actions with open or closed gauge algebras inherently possess local background gauge invariance, especially when anomalies are removable within the antifield formalism, exemplified by chiral W_3 gravity.

Contribution

It establishes a connection between BRST invariance and background gauge invariance in the antifield formalism for theories with open gauge algebras, including anomalous cases.

Findings

BRST invariant actions have background gauge invariance

Anomalies removable in antifield formalism preserve background invariance

Application to chiral W_3 gravity confirms the theoretical framework

Abstract

We show that any BRST invariant quantum action with open or closed gauge algebra has a corresponding local background gauge invariance. If the BRST symmetry is anomalous, but the anomaly can be removed in the antifield formalism, then the effective action possesses a local background gauge invariance. The presence of antifields (BRST sources) is necessary. As an example we analyze chiral $W_3$ gravity.