Bäcklund transformation for supersymmetric self-dual theories for semisimple gauge groups and a hierarchy of $A_1$ solutions

Abstract

We present a Bäcklund transformation (a discrete symmetry transformation) for the self-duality equations for supersymmetric gauge theories in N-extended super-Minkowski space ${\cal M}^{4|4N}$ for an arbitrary semisimple gauge group. For the case of an $A_1$ gauge algebra we integrate the transformation starting with a given solution and iterating the process we construct a hierarchy of explicit solutions.