Perturbatively renormalizable quantum gravity

TL;DR

This paper proposes a perturbatively renormalizable quantum gravity framework by analyzing the conformal factor with a wrong-sign kinetic term, leading to a Hilbert space of interactions that are non-perturbative in Planck's constant.

Contribution

It introduces a novel approach to quantum gravity using the Wilsonian RG and the conformal factor, demonstrating a pathway to renormalizability.

Findings

Supports a Hilbert space of renormalizable interactions with high powers of gravitational fluctuations

Interactions are exponentially suppressed at large field amplitudes

Diffeomorphism invariance is recovered at the boundary of the Hilbert space

Abstract

The Wilsonian renormalization group (RG) requires Euclidean signature. The conformal factor of the metric then has a wrong-sign kinetic term, which has a profound effect on its RG properties. In particular around the Gaussian fixed point, it supports a Hilbert space of renormalizable interactions involving arbitrarily high powers of the gravitational fluctuations. These interactions are characterised by being exponentially suppressed for large field amplitude, perturbative in Newton's constant but non-perturbative in Planck's constant. By taking a limit to the boundary of the Hilbert space, diffeomorphism invariance is recovered whilst retaining renormalizability. Thus the so-called conformal factor instability points the way to constructing a perturbatively renormalizable theory of quantum gravity.