Preferred foliation effects in Quantum General Relativity

TL;DR

This paper explores how Lorentz-violating effects in quantum gravity with a preferred foliation behave under renormalization, finding that Lorentz invariance is a UV fixed point and analyzing matter field effects.

Contribution

It demonstrates that Lorentz violation is a UV attractive fixed point in quantum gravity models with a preferred foliation using functional renormalization group methods.

Findings

Lorentz violation is a UV attractive fixed point.

Matter fields have a small effect on Lorentz violation.

Preferred foliation impacts IR effects in quantum gravity.

Abstract

We investigate the infrared (IR) effects of Lorentz violating terms in the gravitational sector using functional renormalization group methods similar to Reuter and collaborators. The model we consider consists of pure quantum gravity coupled to a preferred foliation, described effectively via a scalar field with non-standard dynamics. We find that vanishing Lorentz violation is a UV attractive fixed-point of this model in the local potential approximation. Since larger truncations may lead to differing results, we study as a first example effects of additional matter fields on the RG running of the Lorentz violating term and provide a general argument why they are small.