Self-Dual Supersymmetric Yang-Mills Theory Generates Witten's Topological Field Theory

Abstract

{}~~~We show that the recently constructed $~N=4$~ supersymmetric self-dual Yang-Mills theory as the consistent background of \hbox{$~N=2$} open superstring will generate Witten's topological field theory in two-dimensions as a descendant theory after appropriate twisted dimensional reduction/truncations. We also show that this topological field theory further generates supersymmetric Korteweg de Vries equations, $~SL(n)\-$Toda theory and $~W_\infty\-$gravity in the $~n\rightarrow\infty$~ limit. Considering also that this topological field theory is to generate other integrable and topological systems, our results give supporting evidence for the conjecture that the $~N=2$~ open superstring theory is the underlying ``master theory'' of integrable and topological systems, {\it via} the intermediate $~N=4$~ supersymmetric self-dual Yang-Mills theory as its consistent target space-time background.