INDUCED POLYAKOV SUPERGRAVITY ON RIEMANN SURFACES OF HIGHER-GENUS

An effective action is obtained for the N = 1, 2D-induced supergravity on a compact super Riemann surface (without boundary) SIGMA of genus g > 1, as the general solution of the corresponding superconformal War d identity. This is accomplished by defining a new super integration t heory on SIGMA which includes a new formulation of the super Stokes th eorem and residue calculus in the superfield formalism. Another crucia l ingredient is the notion of polydromic fields. The resulting action is shown to be well defined and free of singularities on SIGMA. As a b y-product, we point out a morphism between the diffeomorphism symmetry and holomorphic properties.