Some Comments on Dilaton Gravity

TL;DR

This paper investigates a Weyl invariant extension of Einstein gravity, revealing a conformal anomaly in the quantum theory's equations of motion trace, which can be eliminated by choosing an appropriate gauge, affecting diffeomorphism invariance.

Contribution

It introduces a Weyl invariant extension of Einstein gravity and analyzes the presence and gauge-dependent nature of the conformal anomaly in the quantum regime.

Findings

Conformal anomaly appears in the trace of equations of motion.

Anomaly vanishes on-shell, indicating a different gauge choice.

Anomaly can be eliminated off-shell at the cost of losing diffeomorphism invariance.

Abstract

A Weyl invariant extension of Einstein gravity is studied. It simply consists in the group averaging of Einstein's action under Weyl transformations. Contradicting cherished beliefs, a conformal anomaly is found in the trace of the equations of motion if diffeomorphism invariance is to be a symmetry of the quantum theory. This anomaly however vanishes on shell, which signals the existence of another gauge in which the anomaly is absent. It can be made also to vanish off-shell at the price of losing diffeomorphism invariance