Zero Curvature Formalism for Supersymmetric Integrable Hierarchies in Superspace

TL;DR

This paper extends the Drinfeld-Sokolov formalism to superspace, systematically deriving zero curvature formulations for supersymmetric integrable hierarchies using graded algebras and symmetric space methods.

Contribution

It introduces a generalized formalism for supersymmetric integrable systems in superspace, connecting Lax equations to zero curvature conditions with graded algebra structures.

Findings

Derived supersymmetric AKNS hierarchies from zero curvature conditions.

Established Hermitian symmetric space structure for supersymmetric hierarchies.

Unified bosonic and supersymmetric integrable system framework.

Abstract

We generalize the Drinfeld-Sokolov formalism of bosonic integrable hierarchies to superspace, in a way which systematically leads to the zero curvature formulation for the supersymmetric integrable systems starting from the Lax equation in superspace. We use the method of symmetric space as well as the non-Abelian gauge technique to obtain the supersymmetric integrable hierarchies of the AKNS type from the zero curvature condition in superspace with the graded algebras, sl(n+1,n), providing the Hermitian symmetric space structure.