Superstring scattering amplitudes in higher genus

Abstract

In this paper we continue the program pioneered by D'Hoker and Phong, and recently advanced by Cacciatori, Dalla Piazza, and van Geemen, of finding the chiral superstring measure by constructing modular forms satisfying certain factorization constraints. We give new expressions for their proposed ansätze in genera 2 and 3, respectively, which admit a straightforward generalization. We then propose an ansatz in genus 4 and verify that it satisfies the factorization constraints and gives a vanishing cosmological constant. We further conjecture a possible formula for the superstring amplitudes in any genus, subject to the condition that certain modular forms admit holomorphic roots.

Minor changes; final version to appear in Comm. Math. Phys

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Cited by in corpus (34)

• Analytical Solutions of Open String Field Theory
• Modular Forms and Three Loop Superstring Amplitudes
• Tropical Amplitudes
• Remarks on Superstring amplitudes in higher genus
• Superstring loop amplitudes from the field theory limit
• The vanishing of two-point functions for three-loop superstring scattering amplitudes
• Getting superstring amplitudes by degenerating Riemann surfaces
• Superstring measure and non-renormalization of the three-point amplitude
• Classical Codes and Chiral CFTs at Higher Genus
• Genus four superstring measures
• Lattice Theta Constants vs Riemann Theta Constants and NSR Superstring Measures
• Siegel modular forms and finite symplectic groups
• Higher genus partition functions of meromorphic conformal field theories
• One-Dimensional Super Calabi-Yau Manifolds and their Mirrors
• More on superstring chiral measures
• Classical theta constants vs. lattice theta series, and super string partition functions
• Extending the Belavin-Knizhnik "wonderful formula" by the characterization of the Jacobian
• Topics in Two-Loop Superstring Perturbation Theory
• NSR superstring measures in genus 5
• On the pole structures of the disconnected part of hyper elliptic g loop M point super string amplitudes
• The superstring cosmological constant and the Schottky form in genus 5
• Modular Invariant Regularization of String Determinants and the Serre GAGA Principle
• Equidistribution Rates, Closed String Amplitudes, and the Riemann Hypothesis
• Finite Strings From Non-Chiral Mumford Forms
• Boundary contributions to three loop superstring amplitudes
• Uniformization, Unipotent Flows and the Riemann Hypothesis
• Theta characteristics and their moduli
• Calculation and modular properties of multi-loop superstring amplitudes
• Binary Forms and the Hyperelliptic Superstring Ansatz
• The Super Mumford Form and Sato Grassmannian
• Singular Spin Structures and Superstrings
• Construction of chiral superstring measure
• RNS superstring measure for genus 3
• Eluding SUSY at every genus on stable closed string vacua