Asymptotically Safe Gravity-Fermion Systems on Curved Backgrounds

Abstract

We set up a consistent background field formalism for studying the renormalization group (RG) flow of gravity coupled to Nf 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 that breaks chiral symmetry explicitly. Our analysis identified 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 Nf outside of a small window situated at low values Nf and become weakly coupled in the large Nf-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.

Shift-symmetric Horndeski gravity in the asymptotic-safety paradigm

“…Non-trivial evidence is mounting for asymptotic safety in gravity-matter models with Standard-Model fields and interactions, e.g., [32,35,38,97,106,123,127,[131][132][133][134][135][136][137][138][139][140][141]. Additional studies focusing on scalar-gravity models [31,33,34,129,[142][143][144][145][146][147][148][149], fermion-gravity models [150][151][152][153][154][155][156] and vector-gravity models [36,122,[157][158][159][160][161] provide additional support for asymptotic safety in gravity-matter models. Open questions on gravity-matter models are reviewed together with the state-of-the-art in [162].…”

Weak-gravity bound in asymptotically safe gravity-gauge systems

“…Yet, it is, of course, crucial to supplement the analysis by the actual fixed-point values for G and Λ to discover whether or not asymptotic safety evades the weak-gravity bound and passes this critical viability test. The existence of a fixed point for pure gravity has been established in numerous works [71,73,75, and under the inclusion of matter in [14,28,42,54,76,77,139,[144][145][146][147][148][149][150][151][152][153][154][155][156]. To search for fixed points, we use the beta functions for Λ and G [157], supplemented with the matter contributions from [145,148].…”

Grand unification and the Planck scale: An $\mathit{SO}(10)$ example of radiative symmetry breaking

“…As long as all GUEFT couplings c i remain in the perturbative regime, neglecting O(c 2 i ) is a good approximation. Dots denote further terms arising from non-minimal couplings [127][128][129][130][131][132][133] and induced higher-order matter [130,131,[134][135][136][137][138][139][140] couplings.…”