Gauge invariant formulation of $N=2$ Toda and KdV systems in extended superspace

TL;DR

This paper develops a gauge invariant framework for $N=2$ supersymmetric Toda and KdV systems in extended superspace, highlighting superconformal invariance and conserved currents, and extends to non-abelian cases.

Contribution

It introduces a novel gauge invariant formulation of $N=2$ Toda and KdV systems in superspace, including non-abelian extensions, with analysis of superconformal invariance and conserved currents.

Findings

Established gauge invariant $N=2$ Toda equations in superspace

Connected conserved currents with Drinfeld-Sokolov gauges

Extended methods to non-abelian Toda and matrix $N=2$ KdV hierarchies

Abstract

We give a gauge invariant formulation of $N=2$ supersymmetric abelian Toda field equations in \n2 superspace. Superconformal invariance is studied. The conserved currents are shown to be associated with Drinfeld-Sokolov type gauges. The extension to non-abelian \n2 Toda equations is discussed. Very similar methods are then applied to a matrix formulation in \n2 superspace of one of the \n2 KdV hierarchies.