Supersymmetric integrable systems embedded in supersymmetric self-dual Yang-Mills theory

Abstract

We perform dimensional reductions of recently constructed self-dual N=2 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 integrable 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 supersymmetric Yang-Mills theory generates supersymmetric integrable systems in lower dimensions.