A Note on Weyl invariance in gravity and the Wess-Zumino functional

TL;DR

This paper demonstrates how the Wess-Zumino functional can restore Weyl symmetry in gravity by introducing a dilaton field, linking it to the standard Weyl-invariant Einstein-Hilbert action.

Contribution

It provides an explicit calculation of the Wess-Zumino functional for Weyl symmetry breaking in gravity and shows how to restore symmetry with a dilaton field.

Findings

Wess-Zumino functional can restore Weyl symmetry in gravity.

Adding the counter-term reproduces the standard Weyl-invariant action.

The approach may give Einstein-Hilbert action a new theoretical status.

Abstract

It is shown that the explicit calculation of the Wess-Zumino functional pertaining to the breaking term of the Weyl symmetry for the Einstein-Hilbert action allows to restore the Weyl symmetry by introducing the extra dilaton field as Goldstone field. Adding the Wess-Zumino counter-term to the Einstein-Hilbert action reproduces the usual Weyl invariant action used in standard literature. Further consideration might confer to the Einstein-Hilbert action a new status.