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 (SKP) 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 whole hierarchy of the SKP equations of Manin and Radul is generated by geometrical superfield equations of self-dual supersymmetric Yang-Mills theory. 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 subsystems 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.