A remark on quantum gravity

TL;DR

This paper analyzes the Dyson--Schwinger equations in quantum gravity, revealing a structure that suggests gravity may be renormalizable due to its algebraic properties, challenging traditional views on its non-renormalizability.

Contribution

It introduces a new perspective on quantum gravity's renormalizability by examining the structure of Dyson--Schwinger equations and associated Hopf algebra identities.

Findings

All relevant skeletons are of first order in loop number.

Identities generalize Slavnov Taylor identities for gravity.

Gravity may be renormalizable due to Dyson--Schwinger equation structure.

Abstract

We discuss the structure of Dyson--Schwinger equations in quantum gravity and conclude in particular that all relevant skeletons are of first order in the loop number. There is an accompanying sub Hopf algebra on gravity amplitudes equivalent to identities between n-graviton scattering amplitudes which generalize the Slavnov Taylor identities. These identities map the infinite number of charges and finite numbers of skeletons in gravity to an infinite number of skeletons and a finite number of charges needing renormalization. Our analysis suggests that gravity, regarded as a probability conserving but perturbatively non-renormalizable theory, is renormalizable after all, thanks to the structure of its Dyson--Schwinger equations.