A Superspace Formulation of The BV Action for Higher Derivative Theories

TL;DR

This paper develops a superspace formulation of the BV action for higher derivative theories, highlighting their extended BRST and anti-BRST symmetries within a unified geometric framework.

Contribution

It introduces a superspace formalism with one or two Grassmann coordinates to express the BV action with extended BRST and anti-BRST invariance for higher derivative theories.

Findings

The BV action can be written in a manifestly extended BRST invariant superspace formalism.

The action admits a formulation with on-shell extended anti-BRST invariance using two Grassmann coordinates.

The approach clarifies the symmetry structure of higher derivative theories within the BV framework.

Abstract

We first analyze the anti-BRST and double BRST structures of a certain higher derivative theory that has been known to possess BRST symmetry associated with its higher derivative structure. We discuss the invariance of this theory under shift symmetry in the Batalin Vilkovisky (BV) formalism. We show that the action for this theory can be written in a manifestly extended BRST invariant manner in superspace formalism using one Grassmann coordinate. It can also be written in a manifestly extended BRST invariant manner and on-shell manifestly extended anti-BRST invariant manner in superspace formalism using two Grassmann coordinates.