# Abdol Sabor Salek: A curvature bound from gravitational catalysis in thermal backgrounds

A suitable candidate for a UV-complete quantum theory of gravity needs to be compatible with the existence of chiral fermions. Studies of quantum fields in curved spacetime have shown that an external, gravitational background field with negative curvature spontaneously breaks chiral symmetry and leads to the existence of massive fermions on the order of the curvature scale - an effect described as gravitational catalysis. Recent studies came to the conclusion that the inclusion of a Renormalization Group scale can restore chiral symmetry if the ratio of the average curvature of local patches of spacetime to the energy scale obeys a certain bound. In this project, we extend these calculations to finite temperature and analyze how thermal fluctuations affect this bound. By applying these results to the Asymptotic Safety scenario of quantum gravity, we obtain an upper bound for the fermionic matter content of the particle physics sector of our universe.