Gauge invariant renormalizability of quantum gravity

TL;DR

This paper proves that a broad class of diffeomorphism-invariant quantum gravity models are renormalizable in a gauge-invariant manner, ensuring the consistency of their UV divergence structure.

Contribution

It provides a rigorous proof of gauge invariant renormalizability for generic quantum gravity models using the Batalin-Vilkovisky and background field methods.

Findings

UV divergences are covariant local expressions in these models

The proof applies to models without additional anomalous symmetries

Supports the fundamental role of covariance in quantum gravity renormalization

Abstract

The current understanding of renormalization in quantum gravity (QG) is based on the fact that UV divergences of effective actions in the covariant QG models are covariant local expressions. This fundamental statement plays a central role in QG and, therefore, it is important to prove it for the widest possible range of the QG theories. Using the Batalin-Vilkovisky technique and the background field method, we elaborate the proof of gauge invariant renormalizability for a generic model of quantum gravity that is diffeomorphism invariant and does not have additional, potentially anomalous, symmetries.