Fixed point structure of the conformal factor field in quantum gravity

TL;DR

This paper investigates the fixed point structure of the conformal factor in quantum gravity using flow equations, revealing a rich spectrum of fixed points and their implications for asymptotic safety.

Contribution

It demonstrates the equivalence of background independent flow equations to scalar field theory with a wrong sign kinetic term, uncovering novel fixed point properties.

Findings

Presence of a continuum of fixed points with both discrete and continuous spectra

Identification of relevant directions at the fixed points

Deep understanding of properties at the Gaussian fixed point

Abstract

The $\mathcal{O}(\partial^2)$ background independent flow equations for conformally reduced gravity are shown to be equivalent to flow equations naturally adapted to scalar field theory with a wrong sign kinetic term. This sign change is shown to have a profound effect on the renormalization group properties, broadly resulting in a continuum of fixed points supporting both a discrete and a continuous eigenoperator spectrum, the latter always including relevant directions. The properties at the Gaussian fixed point are understood in particular depth, but also detailed studies of the local potential approximation, and the full $\mathcal{O}(\partial^2)$ approximation are given. These results are related to evidence for asymptotic safety found by other authors.