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 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.

Nonvanishing gravitational contribution to matter beta functions for vanishing dimensionful regulators

“…The setting with linear split and Landau gauge α gf → 0 is commonly used when exploring the interplay between gravity and matter couplings within the framework of asymptotically safe quantum gravity [18,21,27,[45][46][47][48][49][50][51][52][53][54][55][56][57], alternative gauge choices and parameterizations are explored in [17,22,[58][59][60]. The impact of matter on the flow of gravitational couplings was investigated in [19,[61][62][63][64][65][66][67][68][69][70][71][72][73][74][75]. (ii) "Unimodular gravity": In this setting, the conformal mode is non-dynamical, and the symmetry group (before breaking by the regulator) is the group of transverse diffeomorphisms [76][77][78][79][80][81][82][83].…”