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.

56 pages, 15 figures

References in corpus (14)

• On the renormalization group flow of f(R)-gravity
• Asymptotically Safe Lorentzian Gravity
• Taming perturbative divergences in asymptotically safe gravity
• Top mass from asymptotic safety
• Ghost anomalous dimension in asymptotically safe quantum gravity
• Matter Induced Bimetric Actions for Gravity
• Quantum gravity and Standard-Model-like fermions
• Correlation functions on a curved background
• $d=4$ as the critical dimensionality of asymptotically safe interactions
• Asymptotically Safe Gravity with Fermions
• Curvature dependence of quantum gravity with scalars
• Global surpluses of spin-base invariant fermions
• Spin-base invariance of Fermions in arbitrary dimensions
• Gravitational catalysis of chiral and color symmetry breaking of quark matter in hyperbolic space