Fate of chiral symmetry in Riemann-Cartan geometry

TL;DR

This paper investigates how chiral symmetry behaves in a gravitational setting with curvature and torsion, finding that torsion alone does not induce gravitational catalysis of chiral symmetry breaking.

Contribution

It provides a detailed analysis of chiral symmetry breaking in Riemann-Cartan geometry using a scale-dependent effective potential from a bosonized NJL model, highlighting the role of torsion.

Findings

Torsion alone does not cause gravitational catalysis.

Weak curvature and torsion regimes do not access deep infrared effects.

Deep infrared analysis shows torsion does not induce chiral symmetry breaking.

Abstract

We study the mechanism of chiral symmetry breaking for fermionic systems in a gravitational background with curvature and torsion. The analysis is based on a scale-dependent effective potential derived from a bosonized version of the Nambu-Jona-Lasino model in a Riemann-Cartan background. We have investigated the fate of chiral symmetry in two different regimes. First, to gain some intuition on the combined effect of curvature and torsion, we investigate the regime of weak curvature and torsion. However, this regime does not access the deep infrared limit, which is essential to answer questions related to the mechanism of gravitational catalysis in fermionic systems. Second, we look at the regime of vanishing curvature and homogeneous torsion. In this case, although we cannot probe the combined effects of curvature and torsion, we can access the deep infrared contributions of the background torsion to the mechanism of chiral symmetry breaking. Our main finding is that, in the scenario where only torsion is present, there is no indication of a mechanism of gravitational catalysis.