Tree-level superstring amplitudes: the Neveu-Schwarz sector

Abstract

Abstract We present a complete computation of superstring scattering amplitudes at tree level, for the case of Neveu-Schwarz insertions. Mathematically, this is to say that we determine explicitly the superstring measure on the moduli space M 0 , n , 0 $$ {\mathcal{M}}_{0,n,0} $$ of super Riemann surfaces of genus zero with n ≥ 3 Neveu-Schwarz punctures. While, of course, an expression for the measure was previously known, we do this from first principles, using the canonically defined super Mumford isomorphism [1]. We thus determine the scattering amplitudes, explicitly in the global coordinates on M 0 , n , 0 $$ {\mathcal{M}}_{0,n,0} $$ , without the need for picture changing operators or ghosts, and are also able to determine canonically the value of the coupling constant. Our computation should be viewed as a step towards performing similar analysis on M 0 , 0 , n $$ {\mathcal{M}}_{0,0,n} $$ , to derive explicit tree-level scattering amplitudes with Ramond insertions.

Keywords

• Differential and Algebraic Geometry
• Superstrings and Heterotic Strings