A superspace formulation of the BV action

TL;DR

This paper develops a superspace formulation of the BV action that maintains invariance under extended BRST and anti-BRST symmetries, providing a unified geometric framework for gauge theories.

Contribution

It introduces a superspace approach to express the BV action with extended BRST and anti-BRST invariance, generalizing previous formulations.

Findings

BV action can be written in a superspace with one Grassmann coordinate for BRST invariance.

Invariance under both BRST and anti-BRST is achieved in a superspace with two Grassmann coordinates.

The formulation clarifies the geometric structure of gauge symmetries in the BV formalism.

Abstract

We show that the BV (Batalin Vilkovisky) action, formulated with an extended BRST symmetry (including the shift symmetry), is also invariant under an extended anti-BRST transformation (where the antifields are the parameters of the transformation), when the gauge fixing Lagrangian is both BRST and anti-BRST invariant. We show that for a general gauge fixing Lagrangian, the BV action can be written in a manifestly extended BRST invariant manner in a superspace with one Grassmann coordinate whereas it can be expressed in a manifestly extended BRST and anti-BRST invariant manner in a superspace with two Grassmann coordinates when the gauge fixing Lagrangian is invariant under both BRST and anti-BRST transformations.