Spontaneous Breaking of Lorentz Symmetry by Ghost Condensation in Perturbative Quantum Gravity

TL;DR

This paper investigates how ghost condensation in perturbative quantum gravity can spontaneously break Lorentz symmetry, modifies BRST symmetries, and explores the on-shell nilpotency restoration of these symmetries.

Contribution

It introduces the analysis of Lorentz symmetry breaking via ghost condensation in quantum gravity within the Curci-Ferrari gauge, highlighting modifications to BRST symmetries and their on-shell properties.

Findings

Lorentz symmetry is spontaneously broken by ghost condensation.

Modified BRST and anti-BRST transformations are not nilpotent off-shell.

Nilpotency of the modified symmetries is restored on-shell.

Abstract

In this paper we will study the spontaneous breakdown of the Lorentz symmetry by ghost condensation in perturbative quantum gravity. Our analysis will be done in the Curci-Ferrari gauge. We will also analyse modification of the BRST and the anti-BRST transformations by the formation of this ghost condensate. It will be shown that even though the modified BRST and the modified anti-BRST transformations are not nilpotent, their nilpotency is restored on-shell.