Universality and symmetry breaking in conformally reduced quantum gravity

TL;DR

This paper investigates the scaling and symmetry properties of conformally reduced quantum gravity using proper-time regulators, revealing stable trajectories and symmetry breaking mechanisms through numerical analysis of the flow near fixed points.

Contribution

It introduces a robust numerical method to analyze the flow structure around the non-Gaussian fixed point in conformal quantum gravity, highlighting stability and symmetry breaking phenomena.

Findings

Renormalization group trajectories are more stable on flat topology.

Ultraviolet flow exhibits a Hopf bifurcation with a limiting cycle.

Spontaneous diffeomorphism symmetry breaking can occur with non-local volume functionals.

Abstract

The scaling properties of quantum gravity are discussed by employing a class of proper-time regulators in the functional flow equation for the conformal factor within the formalism of the background field method. Renormalization group trajectories obtained by projecting the flow on a flat topology are more stable than those obtained from a projection on a spherical topology. In the latter case the ultraviolet flow can be characterized by a Hopf bifurcation with an ultraviolet attractive limiting cycle. Although the possibility of determining the infrared flow for an extended theory space can be severely hampered due to the conformal factor instability, we present a robust numerical approach to study the flow structure around the non-gaussian fixed point as an inverse-problem strategy. In particular it is shown the possibility of having a spontaneous breaking of the diffeomorphism invariance can be realized with non-local functionals of the volume operator.