The effective potential of gauged NJL model in magnetic field

TL;DR

This paper develops a formalism to analyze the phase structure of the gauged NJL model under external magnetic fields, finding that weak magnetic fields do not affect chiral symmetry breaking conditions.

Contribution

It introduces a new formalism for studying the gauged NJL model in external fields and derives the effective potential in weak magnetic fields.

Findings

Weak magnetic fields do not influence chiral symmetry breaking in fixed gauge coupling.

The formalism allows analysis of the phase structure under arbitrary external fields.

An analogy with black hole physics is briefly discussed.

Abstract

The formalism, which permits to study the phase structure of gauged NJL-model for arbitrary external fields, is developed. The effective potential in the gauged NJL model in the weak magnetic field is found. It is shown that in fixed gauge coupling case the weak magnetic field doesn't influence chiral symmetry breaking condition. The analogy with the situation near black hole is briefly mentioned.