Manifestly Supersymmetric Lax Integrable Hierarchies

TL;DR

This paper introduces a systematic method for constructing supersymmetric KP Lax hierarchies in 1+1 dimensions, providing explicit Lax operators and demonstrating supersymmetry invariance, unifying existing models within a comprehensive framework.

Contribution

It develops a new formalism for manifestly supersymmetric Lax hierarchies, including explicit expressions and invariance proofs, unifying previous models under a common approach.

Findings

Explicit Lax operators in terms of superfield eigenfunctions

Automatic invariance under extended supersymmetry

Existing supersymmetric Lax models are encompassed within the new formalism

Abstract

A systematic method of constructing manifestly supersymmetric $1+1$-dimensional KP Lax hierarchies is presented. Closed expressions for the Lax operators in terms of superfield eigenfunctions are obtained. All hierarchy equations being eigenfunction equations are shown to be automatically invariant under the (extended) supersymmetry. The supersymmetric Lax models existing in the literature are found to be contained (up to a gauge equivalence) in our formalism.