The Rise and Fall of Conformal Scalar-Metric Quantum Gravity.
A systematic study of a gravitational action possessing local conformal invariance is undertaken. The spontaneous breaking of the conformal symmetry induces general relativity as an effective long distance limit through the vacuum expectation value of an unphysical scalar field. The Ward identities of the broken theory guarantee the stability of Minkowski spacetime or, equivalently, the vanishing of the cosmological constant to all orders in any consistent perturbation expansion. This result persists when the theory is coupled to the standard U(1) SU(2) SU(3) model with its electroweak symmetry broken by radiative corrections. A particularly natural small parameter is the ratio of the gravitational degrees of freedom to the matter ones, 1/N. In this perturbation expansion the theory is asymptotically free and renormalizable in a simple way. We show that this expansion predicts the spontaneous breaking of local conformal symmetry. Furthermore, all ghost degrees of freedom acquire gauge fixing dependent masses strongly suggesting the unitarity of the theory. A simple prescription is exhibited establishing the classical as well as quantum equivalence between pure metric and conformal scalar-metric gravitational theories. As a result, any Weyl invariant theory is incapable of resolving the cosmological constant problem. Strong arguments indicate that no realistic quantum gravity theory can be constructed possessing local coordinate and conformal invariance.
- Pub Date:
- Physics: Elementary Particles and High Energy