Supersymmetric Soluble Systems Embedded in Supersymmetric Self--Dual Yang--Mills Theory

TL;DR

This paper demonstrates that dimensional reductions of a 2+2 dimensional supersymmetric Yang-Mills theory can embed various exactly solvable supersymmetric systems in lower dimensions, supporting a conjecture about their fundamental connection.

Contribution

It provides the first evidence that 2+2 dimensional self-dual supersymmetric Yang-Mills theory can generate lower-dimensional supersymmetric soluble systems.

Findings

Embedded supersymmetric KdV, Liouville, and Toda equations in reduced models.

Supported the conjecture linking higher-dimensional supersymmetric Yang-Mills to lower-dimensional solvable systems.

Established a new method for deriving integrable supersymmetric systems from higher-dimensional theories.

Abstract

We perform dimensional reductions of recently constructed self-dual $~N=2$~ {\it supersymmetric} Yang-Mills theory in $~2+2\-$dimensions into two-dimensions. We show that the universal equations obtained in these dimensional reductions can embed supersymmetric exactly soluble systems, such as $~N=1$~ and $~N=2$~ supersymmetric Korteweg-de Vries equations, $~N=1$~ supersymmetric Liouville theory or supersymmetric Toda theory. This is the first supporting evidence for the conjecture that the $~2+2\-$dimensional self-dual {\it supersymmetric} Yang-Mills theory generates {\it supersymmetric} soluble systems in lower-dimensions.