On the super Mumford form in the presence of Ramond and Neveu-Schwarz punctures

Abstract

We generalize the result of Voronov (1988) to give an expression for the super Mumford form on the moduli spaces of super Riemann surfaces with Ramond and Neveu–Schwarz punctures. In the Ramond case we take the number of punctures to be large compared to the genus. We consider for the case of Neveu-Schwarz punctures the super Mumford form over the component of the moduli space corresponding to an odd spin structure. The super Mumford form can be used to create a measure whose integral computes scattering amplitudes of superstring theory. We express it in terms of local bases of global sections of tensor powers of the Berezinian line bundle of a family of super Riemann surfaces.