Self duality in super Yang-Mills theories

The self dual condition in superspace is analysed forN=1,2,4 super Yang-Mills theories. A complete solution of all the constraints in terms of a light cone superfieldJ is presented, where the only equation thatJ satisfies is a SUSY generalization of the Yang equation. By reduction of that equation we obtain various two dimensional SUSY models. We introduce the associated linear problem in terms ofJ, whose integrability condition gives us back the super Yang equation and allows us to obtain the Kac-Moody algebra structure of the theory.