Self-duality and the Supersymmetric KdV Hierarchy

TL;DR

This paper demonstrates how the supersymmetric KdV hierarchy can be derived from self-duality conditions in four-dimensional Yang-Mills theory using graded Lie algebras, linking integrable systems with gauge theory.

Contribution

It introduces a novel derivation of the supersymmetric KdV hierarchy from self-duality conditions, connecting supersymmetric integrable systems with four-dimensional gauge theory.

Findings

Derivation of Susy KdV from self-duality in Yang-Mills fields

Formulation of Susy KdV hierarchy as a vanishing curvature condition

Link between Abelian self-duality and supersymmetric integrable equations

Abstract

We show how the supersymmetric KdV equation can be obtained from the self-duality condition on Yang-Mills fields in four dimension associated with the graded Lie algebra OSp(2/1). We also obtain the hierarchy of Susy KdV equations from such a condition. We formulate the Susy KdV hierarchy as a vanishing curvature condition associated with the U(1) group and show how an Abelian self-duality condition in four dimension can also lead to these equations.