Quantum Gravity is Renormalizable near Two Dimensions

TL;DR

This paper demonstrates that quantum gravity can be renormalizable near two dimensions by maintaining volume-preserving diffeomorphisms and imposing conformal invariance, using BRS formalism and anomaly relations.

Contribution

It provides a proof of quantum gravity's renormalizability near two dimensions, combining symmetry preservation with conformal invariance and BRS formalism.

Findings

Quantum gravity is renormalizable near two dimensions.

Maintaining volume-preserving diffeomorphisms is crucial.

Conformal invariance restores general covariance.

Abstract

We prove the renormalizability of quantum gravity near two dimensions. The successful strategy is to keep the volume preserving diffeomorphism as the manifest symmetry of the theory. The general covariance is recovered by further imposing the conformal invariance. The proof utilizes BRS formalism in parallel with Yang-Mills theory. The crucial ingredient of the proof is the relation between the conformal anomaly and the $\beta$ functions.