Asymptotic safety in $O(N)$ scalar models coupled to gravity

TL;DR

This paper investigates the asymptotic safety of O(N) scalar models coupled to gravity, identifying fixed points and the impact of multiple scalars on the gravitational fixed point using different coarse-graining schemes.

Contribution

It extends previous scalar-tensor theory results to O(N) models, analyzing fixed points and the effects of multiple scalars on asymptotic safety.

Findings

Existence of gravitationally dressed Wilson-Fisher fixed point for N>1 in d=3.

Multiple scalars can destabilize the gravitational fixed point with standard cutoff.

Different coarse-graining schemes yield insights into fixed point stability.

Abstract

We extend recent results on scalar-tensor theories to the case of an O(N)-invariant multiplet. Some exact fixed point solutions of the RG flow equations are discussed. We find that also in the functional context, on employing a standard "type-I" cutoff, too many scalars destroy the gravitational fixed point. For d=3 we show the existence of the gravitationally dressed Wilson-Fisher fixed point also for N>1. We discuss also the results of the analysis for a different, scalar-free, coarse-graining scheme.