Possibility of Spontaneous Symmetry Breaking in the Nambu-Jona-Lasinio model with torsion

TL;DR

This paper investigates the Nambu-Jona-Lasinio model in curved space-time with torsion, demonstrating spontaneous symmetry breaking influenced by torsion and analyzing the effective potential and four-fermion interactions.

Contribution

It introduces a new technique to compute the effective potential in the presence of torsion and explores its impact on symmetry breaking and fermion interactions.

Findings

Spontaneous symmetry breaking occurs due to torsion effects.

Effective potential is derived using anomaly-induced action.

Four-fermion coupling varies with torsion.

Abstract

We discuss the Nambu-Jona-Lasinio (NJL) model in curved space-time with torsion in the leading order of the $1/N$ expansion. The effective potential of the torsion sector is calculated using the new technique based on the nonlocal part of anomaly-induced action which was recently found to produce the effective potential in the low-energy limit. The spontaneous symmetry breaking caused by the change of the torsion term is found, confirming the statements known from the existing literature. Furthermore, the gap equation is calculated as a function of curvature and torsion. Finally, the behavior of the effective four fermions coupling constant as a function of the torsion is discussed.