Renormalization flow towards gravitational catalysis in the 3d Gross-Neveu model

TL;DR

This paper investigates how negative curvature in space can induce symmetry breaking in fermionic systems, using the 3d Gross-Neveu model and the functional renormalization group to analyze gravitational catalysis.

Contribution

It provides a renormalization group analysis of gravitational catalysis in the 3d Gross-Neveu model, extending understanding of symmetry breaking on curved spaces.

Findings

Gravitational catalysis leads to chiral symmetry breaking on negatively curved spaces.

The renormalization flow analysis relates gravitational catalysis to magnetic catalysis.

Estimated curvature thresholds for catalysis in finite systems.

Abstract

Catalyzed symmetry breaking arises from a parametric enhancement of critical fluctuations independently of the coupling strength. Symmetry-breaking fermionic long-range fluctuations exhibit such an enhancement on negatively curved spaces, as is known from mean-field studies. We study gravitational catalysis from the viewpoint of the functional renormalization group using the 3d Gross-Neveu model as a specific example. We observe gravitational catalysis towards a phase of broken discrete chiral symmetry both on a maximally symmetric (AdS) and on a purely spatially curved manifold for constant negative curvature (Lobachevsky plane). The resulting picture for gravitational catalysis obtained from the renormalization flow is closely related to that of magnetic catalysis. As an application, we estimate the curvature required for subcritical systems of finite length to acquire a gravitionally catalyzed gap.