The background scale Ward identity in quantum gravity

TL;DR

This paper demonstrates that, through specific parametrization, gauge fixing, and cutoff choices, the background scale Ward identity in quantum gravity aligns with the RG beta functional, leading to a background rescaling invariant flow equation.

Contribution

It introduces a modified flow equation in quantum gravity that combines the Ward identity and RG equation, ensuring invariance under background rescalings.

Findings

The anomalous variation matches the beta functional under certain conditions.

The combined flow equation is explicitly background rescaling invariant.

The approach clarifies the relationship between Ward identities and RG flow in quantum gravity.

Abstract

We show that with suitable choices of parametrization, gauge fixing and cutoff, the anomalous variation of the effective action under global rescalings of the background metric is identical to the derivative with respect to the cutoff, i.e. to the beta functional, as defined by the exact RG equation. The Ward identity and the RG equation can be combined, resulting in a modified flow equation that is manifestly invariant under global background rescalings.