Perturbatively renormalizable quantum gravity

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.

arXiv comment5 pages; Received Honourable mention in Gravity Research Foundation essay competition-2018

References in corpus (1)

• Fixed point structure of the conformal factor field in quantum gravity

Cited by in corpus (7)

• BRST in the Exact RG
• Quantum gravity, renormalizability and diffeomorphism invariance
• Provable properties of asymptotic safety in $f(R)$ approximation
• Renormalization group properties of the conformal mode of a torus
• The continuum limit of quantum gravity at first order in perturbation theory
• The continuum limit of quantum gravity at second order in perturbation theory
• The continuum limit of the conformal sector at second order in perturbation theory