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

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.

LATEX (with all macros), 11 pages, UMDEPP 94-47 (October 1993)

Cited by in corpus (2)

• Noncommutative Self-Dual Supersymmetric Yang-Mills Theory
• Anti-self-dual Maxwell solutions on hyperkähler manifold and N=2 supersymmetric Ashtekar gravity