Quantum Gravity Unit visitor seminar.
Speaker: Prof. Ichiro Oda, University of the Ryukyus
Title: BRST formalism of Weyl conformal gravity in Weyl geometry

Abstract:
I 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, I show that there is a global Poincare-like IOSp(10|10) symmetry. I 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 Poincare 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.