Classical $N=1$ and $N=2$ super W-algebras from a zero-curvature condition

TL;DR

This paper develops a systematic method to derive classical N=1 and N=2 super W-algebras using zero-curvature conditions on superdifferential operators, linking to the Gelfand-Dickey approach.

Contribution

It introduces a new systematic prescription for deriving super W-algebras from superdifferential operators via zero-curvature conditions.

Findings

Derived classical N=1 and N=2 super W-algebras systematically.

Illustrated the method with a non-trivial example beyond N=1 superconformal algebra.

Commented on the relation to Gelfand-Dickey construction.

Abstract

Starting from superdifferential operators in an $N=1$ superfield formulation, we present a systematic prescription for the derivation of classical $N=1$ and $N=2$ super W-algebras by imposing a zero-curvature condition on the connection of the corresponding first order system. We illustrate the procedure on the first non-trivial example (beyond the $N=1$ superconformal algebra) and also comment on the relation with the Gelfand-Dickey construction of $W$-algebras.