Lattice Theta Constants vs Riemann Theta Constants and NSR Superstring Measures

Abstract

We discuss relations between two different representations of hypothetical holomorphic NSR measures, based on two different ways of constructing the semi-modular forms of weight 8. One of these ways is to build forms from the ordinary Riemann theta constants and another -- from the lattice theta constants. We discuss unexpectedly elegant relations between lattice theta constants, corresponding to 16-dimensional self-dual lattices, and Riemann theta constants and present explicit formulae expressing the former ones through the latter. Starting from genus 5 the modular-form approach to construction of NSR measures runs into serious problems and there is a risk that it fails completely already at genus 6.

16 pages

References in corpus (19)

• Two-Loop Superstrings VI: Non-Renormalization Theorems and the 4-Point Function
• Two-Loop Superstrings I, Main Formulas
• Two-Loop Superstrings II, The Chiral Measure on Moduli Space
• Two-Loop Superstrings IV, The Cosmological Constant and Modular Forms
• Two-Loop Superstrings III, Slice Independence and Absence of Ambiguities
• Two-Loop Superstrings V: Gauge Slice Independence of the N-Point Function
• Modular Forms and Three Loop Superstring Amplitudes
• Asyzygies, modular forms, and the superstring measure II
• 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 measure and non-renormalization of the three-point amplitude
• Two loop superstring amplitudes and S_6 representations
• NSR Superstring Measures Revisited
• Genus four superstring measures
• NSR measures on hyperelliptic locus and non-renormalization of 1,2,3-point functions
• Higher genus partition functions of meromorphic conformal field theories
• The superstring cosmological constant and the Schottky form in genus 5

Cited by in corpus (12)

• Getting superstring amplitudes by degenerating Riemann surfaces
• Classical Codes and Chiral CFTs at Higher Genus
• 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
• Superstring field theory in the democratic picture
• Extending the Belavin-Knizhnik "wonderful formula" by the characterization of the Jacobian
• NSR superstring measures in genus 5
• Modular Invariant Regularization of String Determinants and the Serre GAGA Principle
• Finite Strings From Non-Chiral Mumford Forms
• Construction of chiral superstring measure
• RNS superstring measure for genus 3