Renormalized Functional Renormalization Group

TL;DR

This paper introduces a new formulation of the effective average action with a flow equation that maintains consistency between fluctuation and background fields at finite scales, enhancing quantum gravity calculations.

Contribution

It presents a novel version of the effective average action that improves the background field approximation in the asymptotic safety approach to quantum gravity.

Findings

Ensures consistency of fluctuation and background field equations at finite RG scales

Provides a foundation for calculating quantum gravity observables from first principles

Enhances the background field approximation in asymptotic safety

Abstract

We construct a new version of the effective average action together with its flow equation. The construction entails in particular the consistency of fluctuation field and background field equations of motion, even for finite renormalization group scales. Here we focus on the quantum gravity application, while the generalization of this idea to gauge theories is obvious. Our approach has immediate impact on the background field approximation, which is the most prominent approximation scheme within the asymptotic safety scenario. We outline the calculation of quantum gravity observables from first principles using the new effective average action.