THE SUPER-WEIERSTRASS ZETA-FUNCTION AND OPERATOR PRODUCT EXPANSIONS IN 2D-INDUCED SUPERGRAVITY ON THE SUPERTORUS

In order to solve the super-Beltrami equations (SBE) on the supertorus , we construct the quasielliptic Weierstrass zeta-function as the part ial-differential-equation-Cauchy kernel thereon. Using this solution w e compute the stress-energy tensor and Green functions corresponding t o induced supergravity in Polyakov's path integral formalism. This all ows us to recover the corresponding results on the supercomplex plane and the torus. Finally, we discuss generalizations to super-Riemann su rfaces of higher genus.