Super-WZNW with reductions to supersymmetric and fermionic integrable models

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 half integer graded 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)⊗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.