Lax equations in 10-dimensional supersymmetric classical Yang-Mills theories

Abstract

Savelies and the author recently showed that there exists an on-shell light-cone gauge where the nonlinear part of the field equations reduces to a (super) version of the Yang equations that can be solved using methods inspired by those previously developed for the self-dual Yang-Mills equations in four dimensions. Here the analogy between these latter theories and the present ones is extended by writing a set of super linear partial differential equations that have consistency conditions derivable from the supersymmetric Yang Mills equations in 10 dimensions and are analogues of the Belavin-Zakharov Lax pair. In the simplest example of the two-pole ansatz, the same solution-generating techniques work as in the derivation of the multi-instanton solutions in the late 1970s. The present Lax representation, however, is only a consequence of Gn-tead of being equivalent to) the field equations, in contrast to the Belavin-Zakharov Lax pair.