Super--Lax Operator Embedded in Self--Dual Supersymmetric Yang--Mills Theory

TL;DR

This paper demonstrates how the super-Lax operator for a supersymmetric KP equation can be embedded into self-dual supersymmetric Yang-Mills theory in four dimensions, revealing geometric relationships and guiding principles for embedding integrable systems.

Contribution

It establishes a novel embedding of the super-Lax operator into self-dual supersymmetric Yang-Mills theory, linking integrable systems with supersymmetric gauge theories.

Findings

Super-Lax operator embedded in self-dual supersymmetric Yang-Mills theory.

Clarification of geometric relationship between super-Lax operator and super-Sato equation.

Guiding principle for embedding other integrable systems into four-dimensional supersymmetric gauge theories.

Abstract

We show that the super-Lax operator for $~N=1$~ supersymmetric Kadomtsev-Petviashvili equation of Manin and Radul in three-dimensions can be embedded into recently developed self-dual supersymmetric Yang-Mills theory in $~2+2\-$dimensions, based on general features of its underlying super-Lax equation. The differential geometrical relationship in superspace between the embedding principle of the super-Lax operator and its associated super-Sato equation is clarified. This result provides a good guiding principle for the embedding of other integrable sub-systems in the super-Lax equation into the four-dimensional self-dual supersymmetric Yang-Mills theory, which is the consistent background for $~N=2$~ superstring theory, and potentially generates other unknown supersymmetric integrable models in lower-dimensions.