Asyzygies, modular forms, and the superstring measure II

Abstract

Precise factorization constraints are formulated for the three-loop superstring chiral measure, in the separating degeneration limit. Several natural Ansätze in terms of polynomials in theta constants for the density of the measure are examined. None of these Ansätze turns out to satisfy the dual criteria of modular covariance of weight 6, and of tending to the desired degeneration limit. However, an Ansatz is found which does satisfy these criteria for the square of the density of the measure, raising the possibility that it is not the density of the measure, but its square which is a polynomial in theta constants. A key notion is that of totally asyzygous sextets of spin structures. It is argued that the Ansatz produces a vanishing cosmological constant.

arXiv comment41 pages

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Cited by in corpus (38)

• Modular Forms and Three Loop Superstring Amplitudes
• Superstring scattering amplitudes in higher genus
• Asyzygies, modular forms, and the superstring measure I
• Remarks on Superstring amplitudes in higher genus
• Two-Loop Superstrings VII, Cohomology of Chiral Amplitudes
• Superstring loop amplitudes from the field theory limit
• Superstring measure and non-renormalization of the three-point amplitude
• Getting superstring amplitudes by degenerating Riemann surfaces
• The vanishing of two-point functions for three-loop superstring scattering amplitudes
• Two loop superstring amplitudes and S_6 representations
• Classical Codes and Chiral CFTs at Higher Genus
• Two-loop vacuum energy for Calabi-Yau orbifold models
• Genus four superstring measures
• NSR Superstring Measures Revisited
• Lattice Theta Constants vs Riemann Theta Constants and NSR Superstring Measures
• NSR measures on hyperelliptic locus and non-renormalization of 1,2,3-point functions
• Siegel modular forms and finite symplectic groups
• 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
• Factorization of the Two Loop Four-Particle Amplitude in Superstring Theory Revisited
• Extending the Belavin-Knizhnik "wonderful formula" by the characterization of the Jacobian
• Topics in Two-Loop Superstring Perturbation Theory
• The superstring cosmological constant and the Schottky form in genus 5
• NSR superstring measures in genus 5
• Modular Invariant Regularization of String Determinants and the Serre GAGA Principle
• Equidistribution Rates, Closed String Amplitudes, and the Riemann Hypothesis
• Factorization and Unitarity in Superstring Theory
• Complex Geometry and Supergeometry
• Integrability in String Theories
• The Singular Locus of the Theta Divisor and Quadrics through a Canonical Curve
• Finite Strings From Non-Chiral Mumford Forms
• Boundary contributions to three loop superstring amplitudes
• A Formula for Multi-Loop 4-Particle Amplitude in Superstring Theory
• Binary Forms and the Hyperelliptic Superstring Ansatz
• Eluding SUSY at every genus on stable closed string vacua
• Construction of chiral superstring measure
• RNS superstring measure for genus 3