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 the 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 ∞-gravity in the n→∞ limit. Considering also that this topological field theory is to generate other integrable and topological systems, our resutls give supporting evidence for the conjecture that the N=2 open superstring theory is the underlying “master theory” of integrable and topological systems, via the intermediate N=4 supersymmetric self-dual Yang-Mills theory as its consistent target space-time background.