Perturbative quantum gravity in Batalin-Vilkovisky formalism

TL;DR

This paper develops a supermanifold and superspace formulation of perturbative quantum gravity using the Batalin-Vilkovisky formalism, incorporating BRST, anti-BRST, and shift symmetries, and translating the quantum master equation into a superfield structure.

Contribution

It introduces a superfield approach to BV quantization of perturbative quantum gravity with combined BRST, anti-BRST, and shift symmetries, extending the formalism into superspace.

Findings

BV action realized as Grassmann translation

Quantum master equation expressed as superfield

Construction of BRST and anti-BRST invariant BV action in superspace

Abstract

In this Letter we consider the perturbative quantum gravity on the super-manifold which remains invariant under absolutely anticommuting BRST and anti-BRST transformations. In addition to that the theory posses one more symmetry known as shift symmetry. The BRST invariant Batalin-Vilkovisky (BV) action for perturbative quantum gravity is realized as a translation in Grassmann coordinate. Further we show that the quantum master equation of the BV quantization method at one-loop order can be translated to have a superfield structure for the action. However, the BRST as well as anti-BRST invariant BV action is constructed in superspace with the help of two Grassmann coordinates.