Duality study of chiral Heisenberg Gross-Neveu model in 1+1 dimensions

TL;DR

This paper analyzes a 1+1 dimensional chiral Heisenberg Gross-Neveu model, revealing spontaneous symmetry breaking, duality to the Nambu--Jona-Lasinio model, and detailed phase diagrams including effects of a bare mass term.

Contribution

It demonstrates a duality to the NJL model and explores the phase structure of the chiral Heisenberg Gross-Neveu model with various parameters.

Findings

Spontaneous symmetry breaking with massless and massive bosons

Duality to the NJL model with isospin

Phase diagram as a function of temperature, chemical potential, and isospin

Abstract

We consider a version of the Gross-Neveu model in 1+1 dimensions with discrete chiral and continuous flavor symmetry (isospin). In 2+1 dimensions, this model is known as chiral Heisenberg Gross-Neveu model. Spontaneous symmetry breaking and the emergence of two massless and one massive scalar bosons are shown. A duality to the Nambu--Jona-Lasinio model with isospin is exhibited, provided that the isovector pseudoscalar mean field is constrained to a plane in isospin space. This enables us to find the phase diagram as a function of temperature, chemical potential and isospin chemical potential as well as twisted kinks. A bare mass term acts quite differently when added to this model as compared to other chiral variants of the Gross-Neveu model.