Tree-level superstring amplitudes: the Neveu-Schwarz sector

• Published in: The journal of high energy physics 2024-09, Vol.2024 (9), p.8-32, Article 8
• Main Authors: Cacciatori, Sergio L., Grushevsky, Samuel, Voronov, Alexander A.
• Format: Article
• Language: English
• Subjects: Amplitudes; Classical and Quantum Gravitation; Computation; Differential and Algebraic Geometry; Elementary Particles; First principles; Isomorphism; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Riemann surfaces; Scattering; Spacetime; String Theory; Superstrings and Heterotic Strings; Topological manifolds
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP09(2024)008

A bstract 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 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 , 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 , to derive explicit tree-level scattering amplitudes with Ramond insertions.