BRST Formalism of Weyl Conformal Gravity

TL;DR

This paper develops the BRST formalism for Weyl conformal gravity, revealing supersymmetry, spontaneous symmetry breaking, and demonstrating unitarity of the quantum theory.

Contribution

It introduces a novel BRST framework for Weyl conformal gravity, including gauge-fixing conditions and symmetry analysis, highlighting spontaneous symmetry breaking and unitarity.

Findings

Existence of Poincaré-like supersymmetry in the model

Spontaneous breaking of Weyl symmetry to Poincaré symmetry

Proof of unitarity of the physical S-matrix

Abstract

We present the BRST formalism of a Weyl conformal gravity in Weyl geometry. Choosing the extended de Donder gauge-fixing condition (or harmonic gauge condition) for the general coordinate invariance and the new scalar gauge-fixing for the Weyl invariance we find that there is a Poincar${\rm{\acute{e}}}$-like $\IOSp(10|10)$ supersymmetry as in a Weyl invariant scalar-tensor gravity in Riemann geometry. We also point out that there is a gravitational conformal symmetry in quantum gravity although there is a massive Weyl gauge field as a result of spontaneous symmetry breakdown of Weyl gauge symmetry and account for how the gravitational conformal symmetry is spontaneously broken to the Poincar\'e symmetry. The corresponding massless Nambu-Goldstone bosons are the graviton and the dilaton. We also prove the unitarity of the physical S-matrix on the basis of the BRST quartet mechanism.