B\"acklund transformation for supersymmetric self-dual theories for semisimple gauge groups and a hierarchy of $A_1$ solutions

TL;DR

This paper introduces a B"acklund transformation for supersymmetric self-duality equations in super-Minkowski space, enabling the generation of a hierarchy of explicit solutions for semisimple gauge groups, especially for the $A_1$ case.

Contribution

It presents a novel B"acklund transformation applicable to supersymmetric self-dual gauge theories with arbitrary semisimple gauge groups, and constructs explicit solution hierarchies for the $A_1$ case.

Findings

Developed a B"acklund transformation for supersymmetric self-duality equations.

Constructed a hierarchy of explicit solutions for the $A_1$ gauge algebra.

Extended the transformation to arbitrary semisimple gauge groups.

Abstract

We present a B\"acklund 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.