Dynamical symmetry breaking in the external gravitational and constant magnetic fields

TL;DR

This paper studies how external gravitational and magnetic fields influence dynamical symmetry breaking in NJL and SUSY NJL models, revealing that curvature and magnetic fields can both suppress and induce chiral symmetry breaking.

Contribution

It provides explicit Green functions and effective potentials in curved spacetime with magnetic fields, analyzing their impact on phase transitions in these models.

Findings

Increased curvature reduces chiral symmetry breaking.

Strong magnetic fields induce symmetry breaking even with fixed curvature.

External fields significantly alter the phase structure of the models.

Abstract

We investigate the effects of the external gravitational and constant magnetic fields to the dynamical symmetrybreaking. As simple models of the dynamical symmetry breaking we consider the Nambu-Jona-Lasinio (NJL) model and the supersymmetric Nambu-Jona-Lasinio (SUSY NJL) model non-minimally interacting with the external gravitational field and minimally interacting with constant magnetic field. The explicit expressions for the scalar and spinor Green functions are found up to the linear terms on the spacetime curvature and exactly for a constant magnetic field. We obtain the effective potential of the above models from the Green functions in the magnetic field in curved spacetime. Calculating the effective potential numerically with the varying curvature and/or magnetic fields we show the effects of the external gravitational and magnetic fields to the phase structure of the theories. In particular, increase of the curvature in the spontaneously broken chiral symmetry phase due to the fixed magnetic field makes this phase to be less broken. On the same time strong magnetic field quickly induces chiral symmetry breaking even at the presence of fixed gravitational field within nonbroken phase.