A curvature bound from gravitational catalysis

Understand

We determine bounds on the curvature of local patches of spacetime from the requirement of intact long-range chiral symmetry.

• The bounds arise from a scale-dependent analysis of gravitational catalysis and its influence on the effective potential for the chiral order parameter, as induced by fermionic fluctuations on a curved spacetime with local hyperbolic properties.
• The bound is expressed in terms of the local curvature scalar measured in units of a gauge-invariant coarse-graining scale.
• We argue that any effective field theory of quantum gravity obeying this curvature bound is safe from chiral symmetry breaking through gravitational catalysis and thus compatible with the simultaneous existence of chiral fermions in the low-energy spectrum.