Nambu-Jona-Lasinio Model in Curved Spacetime with Magnetic Field

TL;DR

This paper investigates how curved spacetime and magnetic fields influence chiral symmetry breaking in the NJL model, revealing that gravity can counteract magnetic effects and restore symmetry.

Contribution

It introduces a detailed analysis of the NJL model in curved spacetime with magnetic fields, including effective potential calculations and numerical studies of chiral symmetry.

Findings

Gravitational fields can offset magnetic field effects on chiral symmetry.

Chiral symmetry can be restored by curvature despite magnetic field presence.

Effective potential is computed for various curvature and magnetic field conditions.

Abstract

We discuss the phase structure of the NJL model in curved spacetime with magnetic field using $1/N$-expansion and linear curvature approximation. The effective potential for composite fields $\bar\psi \psi$ is calculated using the proper-time cut-off in the following cases: a) at non-zero curvature, b) at non-zero curvature and non-zero magnetic field, and c) at non-zero curvature and non-zero covariantly constant gauge field. Chiral symmetry breaking is studied numerically. We show that the gravitational field may compensate the effect of the magnetic field what leads to restoration of chiral symmetry.