Super WZNW with Reductions to Supersymmetric and Fermionic Integrable Models

TL;DR

This paper presents a systematic approach to constructing supersymmetric and fermionic integrable models using gauged WZNW models linked to twisted affine Kac-Moody algebras, with explicit examples including super sinh-Gordon and Gross-Neveu models.

Contribution

It introduces a new systematic construction method for supersymmetric and fermionic integrable models via gauged WZNW models and provides detailed examples and conditions for integrability.

Findings

Explicit construction of super sinh-Gordon models.

Identification of fermionic theories from specific cosets.

Connection to known models like Gross-Neveu and Thirring.

Abstract

A systematic construction for an action describing a class of supersymmetric integrable models as well as for pure fermionic theories is discussed in terms of the gauged WZNW model associated to twisted affine Kac-Moody algebras. Explicit examples of the $N=1,2$ super sinh(sine)-Gordon models are discussed in detail. Pure fermionic theories arises for cosets $sl(p,1)/sl(p)\otimes u(1)$ when a maximal kernel condition is fulfilled. The integrability condition for such models is discussed and it is shown that the simplest example when $p=2$ leads to the constrained Bukhvostov-Lipatov, Thirring, scalar massive and pseudo-scalar massless Gross-Neveu models.