SUPERHOLOMORPHIC STRUCTURES, MOMENT MAPS, AND SUPER SELF-DUAL YANG-MILLS CONNECTIONS OVER SUPER RIEMANN SURFACES

We consider the space of superconnections with certain curvature constraints over super Riemann surfaces. We define a moment map over that space to the dual of the super Lie algebra of gauge transformations. The zero set of this moment map corresponds to the super self-dual Yang-Mills equations in two dimensions. This result generalizes the recently proposed scheme for the nonsupersymmetric case. The superfield equations also arise from super self-dual Yang-Mills equations in four dimensions by dimensional reduction. © 1990 Kluwer Academic Publishers.