Current algebras on super-Riemann surfaces

Two-dimensional N=1 supersymmetric Yang-Mills theory is formulated in superspace, to examine the Ward identities for super Kac-Moody algebras on super-Riemann surfaces of genus g (≥ 2) in the path-integral formalism. To derive Green kernels, we use the theory of automorphic functions on super-Riemann surfaces in the Schottky parametrization. The Ward indentities are expressed in terms of the Poincare theta series. (orig.)