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

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.

11 pages, 2 figures

References in corpus (4)

• Self-consistent multiple complex-kink solutions in Bogoliubov-de Gennes and chiral Gross-Neveu systems
• Phase structure of the 1+1 dimensional Nambu--Jona-Lasinio model with isospin
• Duality between chiral symmetry breaking and charged pion condensation at large $N_c$: Consideration of an NJL${}_2$ model with baryon-, isospin- and chiral isospin chemical potentials
• Beyond integrability: Baryon-baryon backward scattering in the massive Gross-Neveu model

Cited by in corpus (7)

• Absence of inhomogeneous chiral phases in 2+1-dimensional four-fermion and Yukawa models
• Stability of homogeneous chiral phases against inhomogeneous perturbations in 2+1 dimensions
• Spatially oscillating correlation functions in $\left(2+1\right)$-dimensional four-fermion models: The mixing of scalar and vector modes at finite density
• Functional renormalization of QCD in $1+1$ dimensions: four-fermion interactions from quark-gluon dynamics
• Dark solitons of the Gross-Neveu model
• Existence of a supersymmetric extension of the gauged non-linear $\Sigma$-model and the transition from integrability to chaos
• Detecting inhomogeneous chiral condensation from the bosonic two-point function in the $(1+1)$-dimensional Gross-Neveu model in the mean-field approximation