BRST and Anti-BRST Symmetries in Perturbative Quantum Gravity

TL;DR

This paper explores the properties of BRST and anti-BRST symmetries in perturbative quantum gravity, analyzing their invariance, gauge dependence, and effects of mass terms in curved spacetime.

Contribution

It provides a detailed analysis of BRST and anti-BRST symmetries in curved spacetime, including gauge dependence and the impact of mass terms on their nilpotency.

Findings

BRST and anti-BRST invariance holds in perturbative quantum gravity.

Gauge fixing terms can be expressed as total BRST or anti-BRST variations in certain gauges.

Mass terms violate the nilpotency of BRST and anti-BRST transformations.

Abstract

In perturbative quantum gravity, the sum of the classical Lagrangian density, a gauge fixing term and a ghost term is invariant under two sets of supersymmetric transformations called the BRST and the anti-BRST transformations. In this paper we will analyse the BRST and the anti-BRST symmetries of perturbative quantum gravity in curved spacetime, in linear as well as non-linear gauges. We will show that even though the sum of ghost term and the gauge fixing term can always be expressed as a total BRST or a total anti-BRST variation, we can express it as a combination of both of them only in certain special gauges. We will also analyse the violation of nilpotency of the BRST and the anti-BRST transformations by introduction of a bare mass term, in the massive Curci-Ferrari gauge.