Quantum Scale Invariant Gravity with de Donder Gauge

TL;DR

This paper develops a covariant quantization framework for scale-invariant gravity with a scalar field in de Donder gauge, revealing underlying symmetries and the massless nature of the dilaton as a Nambu-Goldstone boson.

Contribution

It introduces a manifestly covariant quantization method for scale-invariant gravity, deriving equal-time commutation relations and uncovering choral symmetry and spontaneous scale symmetry breaking.

Findings

Derivation of equal-time commutation relations in de Donder gauge

Identification of choral symmetry as IOSp(8|8) supersymmetry

Demonstration that the dilaton is a massless Nambu-Goldstone particle

Abstract

We perform the manifestly covariant quantization of a scale invariant gravity with a scalar field, which is equivalent to the well-known Brans-Dicke gravity via a field redefinition of the scalar field, in the de Donder gauge condition (or harmonic gauge condition) for general coordinate invariance. First, without specifying the expression of a gravitational theory, we write down various equal-time (anti-)commutation relations (ETCRs), in particular, those involving the Nakanishi-Lautrup field, the FP ghost, and the FP antighost only on the basis of the de Donder gauge condition. It is shown that choral symmetry, which is a Poincar${\rm{\acute{e}}}$-like $IOSp(8|8)$ supersymmetry, can be derived from such a general action with the de Donder gauge. Next, taking the scale invariant gravity with a scalar field as a classical theory, we derive the ETCRs for the gravitational sector involving the metric tensor and scalar fields. Moreover, we account for how scale symmetry is spontaneously broken in quantum gravity, thereby showing that the dilaton is a massless Nambu-Goldstone particle.