Asymptotically Safe Gravity-Fermion systems on curved backgrounds

Understand

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.