Progress in classically solving ten dimensional supersymmetric reduced Yang-Mills theories

TL;DR

This paper develops methods to solve ten-dimensional supersymmetric reduced Yang-Mills theories by simplifying fermionic components and deriving solutions in reduced dimensions, extending techniques from bosonic self-dual Yang-Mills equations.

Contribution

It introduces an on-shell light cone gauge simplifying fermionic components and derives solutions for reduced supersymmetric Yang-Mills theories using adapted techniques.

Findings

Half of the fermionic components vanish in the chosen gauge.

General solutions are derived for the linearized subset of equations.

Non-linear equations are solvable using methods similar to those for self-dual Yang-Mills.

Abstract

It is shown that there exists an on-shell light cone gauge where half of the fermionic components of the super vector potential vanish, so that part of the superspace flatness conditions becomes linear. After reduction to $(1+1)$ space-time dimensions, the general solution of this subset of equations is derived. The remaining non-linear equations are written in a form which is analogous to Yang equations, albeit with superderivatives involving sixteen fermionic coordinates. It is shown that this non-linear part may, nevertheless, be solved by methods similar to powerful technics previously developed for the (purely bosonic) self-dual Yang Mills equations in four dimensions.