A curvature bound from gravitational catalysis

TL;DR

This paper establishes bounds on spacetime curvature to prevent gravitational catalysis from breaking chiral symmetry, ensuring compatibility of chiral fermions with quantum gravity theories.

Contribution

It introduces a scale-dependent curvature bound derived from gravitational catalysis effects, linking spacetime geometry to chiral symmetry preservation in quantum gravity.

Findings

Curvature bounds depend on local hyperbolic properties of spacetime.

Bounds become more restrictive with higher dimensions.

Application to asymptotic safety constrains particle physics models.

Abstract

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. With increasing number of dimensions, the curvature bound in terms of the hyperbolic scale parameter becomes stronger. Applying the curvature bound to the asymptotic safety scenario for quantum gravity in four spacetime dimensions translates into bounds on the matter content of particle physics models.