Punctures on super Riemann surfaces

Abstract

An investigation of the geometry of punctured super Riemann surfaces and their moduli is pursued with particular emphasis on Ramond (or spin) punctures. A central role is played by the notion of a standard punctured neighborhood, which may be glued into a super Riemann surface to create a punctured surface. A geometrical explanation is given for the rule that two Ramond punctures only have one odd modulus. Explicit examples of spheres with Ramond and Neveu-Schwarz punctures are constructed and the connection between moduli of punctures and picture changing is elaborated. This description of punctures combined with the operator formalism should be useful both in treating fermionic or (R, R) sector backgrounds for the superstring and in the unitarity proof for the superstring.