Supersymmetric Moyal-Lax Representations

TL;DR

This paper introduces the super Moyal-Lax representation and super Moyal momentum algebra, systematically analyzing supersymmetric integrable models and their properties, including Hamiltonian structure and dispersionless limits.

Contribution

It presents the super Moyal-Lax framework and explores its implications for supersymmetric integrable systems, extending bosonic results to supersymmetric cases.

Findings

Super Moyal-Lax equation can be derived from an action.

Parameter of non-commutativity relates to the central charge.

Dispersionless limit of supersymmetric models is accessible.

Abstract

The super Moyal-Lax representation and the super Moyal momentum algebra are introduced and the properties of simple and extended supersymmetric integrable models are systematically investigated. It is shown that, much like in the bosonic cases, the super Moyal-Lax equation can be interpreted as a Hamiltonian equation and can be derived from an action. Similarly, we show that the parameter of non-commutativity, in this case, is related to the central charge of the second Hamiltonian structure of the system. The super Moyal-Lax description allows us to go to the dispersionless limit of these models in a singular limit and we discuss some of the properties of such systems.