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) Σ̂ of genus g > 1, as the general solution of the corresponding superconformal Ward identity. This is accomplished by defining a new super integration theory on Σ̂ which includes a new formulation of the super Stokes theorem and residue calculus in the superfield formalism. Another crucial ingredient is the notion of polydromic fields. The resulting action is shown to be well-defined and free of singularities on Σ̂. As a by-product, we point out a morphism between the diffeomorphism symmetry and holomorphic properties. LPTB 93-10 hep-th/9310163 September 1993 PACS 04.65.,11.30.p Email addresses: [email protected],[email protected] † UnitΘ AssociΘe au CNRS, U.A.764