Asymptotically Safe Gravity with Fermions

TL;DR

This paper investigates the fixed point structure of gravity coupled with fermions using the functional renormalization group, revealing two families of fixed points with different bounds on fermion number, crucial for asymptotic safety.

Contribution

It introduces a novel truncation scheme incorporating non-minimal gravity-fermion interactions, clarifies regulator dependence issues, and extends fixed point analysis to curved backgrounds.

Findings

Two families of fixed points identified, with one having an upper fermion bound.

Non-minimal interactions are essential for distinguishing fixed point families.

Clarified regulator dependence and compared with flat background studies.

Abstract

We use the functional renormalization group equation for the effective average action to study the fixed point structure of gravity-fermion systems on a curved background spacetime. We approximate the effective average action by the Einstein-Hilbert action supplemented by a fermion kinetic term and a coupling of the fermion bilinears to the spacetime curvature. The latter interaction is singled out based on a "smart truncation building principle". The resulting renormalization group flow possesses two families of interacting renormalization group fixed points extending to any number of fermions. The first family exhibits an upper bound on the number of fermions for which the fixed points could provide a phenomenologically interesting high-energy completion via the asymptotic safety mechanism. The second family comes without such a bound. The inclusion of the non-minimal gravity-matter interaction is crucial for discriminating the two families. Our work also clarifies the origin of the strong regulator-dependence of the fixed point structure reported in earlier literature and we comment on the relation of our findings to studies of the same system based on a vertex expansion of the effective average action around a flat background spacetime.