# Gauge invariant renormalizability of quantum gravity

## TL;DR

This paper proves that quantum gravity models invariant under diffeomorphisms remain gauge invariant and renormalizable at all loop orders using the Batalin-Vilkovisky and background field methods.

## Contribution

It demonstrates gauge invariant renormalizability of generic diffeomorphism-invariant quantum gravity models without anomalies, ensuring control over gauge symmetry deformations at all loop levels.

## Key findings

- Gauge invariant renormalizability established for quantum gravity.
- Control over gauge symmetry deformations at all loop orders.
- Maintains general covariance of divergent effective action parts.

## Abstract

Using the Batalin-Vilkovisky technique and the background field method the proof of gauge invariant renormalizability is elaborated for a generic model of quantum gravity which is diffeomorphism invariant and has no other, potentially anomalous, symmetries. The gauge invariant renormalizability means that in all orders of loop expansion of the quantum effective action one can control deformations of the generators of gauge transformations which leave such an action invariant. In quantum gravity this means that one can maintain general covariance of the divergent part of effective action when the mean quantum field, ghosts and antifields are switched off.