BRST Formalism of Weyl Invariant Gravity

by Ichiro Oda (Ryukyus U.)

Wednesday 13 Sept 2023, 14:30 → 15:30 Europe/Rome

1/1-2 - Aula "C. Voci" (Dipartimento di Fisica e Astronomia - Edificio Marzolo)

We construct a BRST formalism of Weyl invariant gravity by taking the extended de Donder gauge for general coordinate invariance and the scalar gauge for Weyl invariance. We point out the existence of a huge global symmetry, IOSp(10|10) symmetry, and show that there is a gravitational conformal symmetry as a subgroup. If we introduce a flat Minkowski metric in our formalism, we can construct a well-known "conformal symmetry" in four space-time dimensions. We then investigate a spontaneous symmetry breakdown of the gravitational conformal symmetry. We find that GL(4) symmetry is spontaneously broken down to the Lorentz symmetry, where  the Nambu-Goldstone boson is nothing but the graviton. Thus, we can prove that the graviton must be exactly massless at the non-perturbative level by following the Nambu-Goldstone theorem. Similarly, special conformal symmetry and dilatation  are also spontaneously broken where the Nambu-Goldstone  boson is the dilaton. Thus, the dilaton must be exactly  massless as well. Finally, by using the Kugo-Ojima BRST quartet mechanism, we show that the physical mode is only  the massless graviton whereas the other particles including the dilaton belong to unphysical sector. Hence, the dilaton  is confined in the unphysical sector as the Faddeev-Popov  ghosts are in Yang-Mills theory, so we are free from the well-known fifth-force problem.