Asymptotically Safe Gravity-Fermion systems on curved backgrounds

TL;DR

This paper investigates the renormalization group flow of gravity coupled to fermions on curved backgrounds, identifying fixed points that support asymptotic safety and exploring symmetry restoration mechanisms.

Contribution

It introduces a background field formalism for gravity-fermion systems and finds new fixed points relevant for asymptotic safety in quantum gravity.

Findings

Identifies two families of RG fixed points suitable for high-energy completion.

Fixed points exist for all but very low fermion numbers and become weakly coupled at large N_f.

Demonstrates possible crossover from non-chiral to chiral fixed points, hinting at symmetry restoration.

Abstract

We set up a consistent background field formalism for studying the renormalization group (RG) flow of gravity coupled to $N_f$ Dirac fermions on maximally symmetric backgrounds. Based on Wetterich's equation we perform a detailed study of the resulting fixed point structure in a projection including the Einstein-Hilbert action, the fermion anomalous dimension, and a specific coupling of the fermion bilinears to the spacetime curvature. The latter constitutes a mass-type term which breaks chiral symmetry explicitly. Our analysis identifies two infinite families of interacting RG fixed points which are viable candidates to provide a high-energy completion through the asymptotic safety mechanism. The fixed points exist for all values of $N_f$ outside of a small window situated at low values $N_f$ and become weakly coupled in the large $N_f$-limit. Symmetry-wise, they correspond to "quasi-chiral" and "non-chiral" fixed points. The former come with enhanced predictive power, fixing one of the couplings via the asymptotic safety condition. Moreover, the interplay of the fixed points allows for cross-overs from the non-chiral to the chiral fixed point, giving a dynamical mechanism for restoring the symmetry approximately at intermediate scales. Our discussion of chiral symmetry breaking effects provides strong indications that the topology of spacetime plays a crucial role when analyzing whether quantum gravity admits light chiral fermions.