The vanishing of two-point functions for three-loop superstring scattering amplitudes

Abstract

In this paper we show that the two-point function for the three-loop chiral superstring measure ansatz proposed by Cacciatori, Dalla Piazza, and van Geemen vanishes. Our proof uses the reformulation of ansatz in terms of even cosets, theta functions, and specifically the theory of the ${\Gamma }_{00}$ linear system on Jacobians introduced by van Geemen and van der Geer. At the two-loop level, where the amplitudes were computed by D'Hoker and Phong, we give a new proof of the vanishing of the two-point function (which was proven by them). We also discuss the possible approaches to proving the vanishing of the two-point function for the proposed ansatz in higher genera.

References in corpus (8)

• Modular Forms and Three Loop Superstring Amplitudes
• Superstring scattering amplitudes in higher genus
• Remarks on Superstring amplitudes in higher genus
• Superstring measure and non-renormalization of the three-point amplitude
• NSR Superstring Measures Revisited
• Genus four superstring measures
• NSR measures on hyperelliptic locus and non-renormalization of 1,2,3-point functions
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• More on superstring chiral measures
• Extending the Belavin-Knizhnik "wonderful formula" by the characterization of the Jacobian
• The superstring cosmological constant and the Schottky form in genus 5
• Modular Invariant Regularization of String Determinants and the Serre GAGA Principle
• Non-analytic terms of string amplitudes from partial waves
• The Gauss map and secants of the Kummer variety
• Finite Strings From Non-Chiral Mumford Forms
• Uniformization, Unipotent Flows and the Riemann Hypothesis
• The Scorza correspondence in genus 3
• Construction of chiral superstring measure
• Singular Spin Structures and Superstrings
• Eluding SUSY at every genus on stable closed string vacua