Z_2-reductions of spinor models in two dimensions

TL;DR

This paper introduces new integrable spinor models in two dimensions, generalizing existing models related to SU(N), SP(2N), and SO(N), and provides a method for their Lax representation construction.

Contribution

It proposes novel integrable spinor models and a systematic method for constructing their Lax representations, expanding the class of known integrable systems.

Findings

New integrable spinor models related to SU(N), SP(2N), and SO(N)

Method for constructing Lax representations of these models

Outline of spectral properties of the Lax operators

Abstract

We propose new types of integrable spinor models, generalizing the well known ones of: i) Nambu-Jona-Lasinio-Vaks-Larkin models, related to SU(N); ii) the Gross-Neveu models - SP(2N); and the iii) Zakharov-Mikhailov models - SO(N). We propose a method for constructing their Lax representation and outline the spectral properties of the Lax operators.