Classical theta constants vs. lattice theta series, and super string partition functions

Abstract

Recently, various possible expressions for the vacuum-to-vacuum superstring amplitudes has been proposed at genus $g=3,4,5$. To compare the different proposals, here we will present a careful analysis of the comparison between the two main technical tools adopted to realize the proposals: the classical theta constants and the lattice theta series. We compute the relevant Fourier coefficients in order to relate the two spaces. We will prove the equivalence up to genus 4. In genus five we will show that the solutions are equivalent modulo the Schottky form and coincide if we impose the vanishing of the cosmological constant.

21 pages

References in corpus (15)

• 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
• 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
• Getting superstring amplitudes by degenerating Riemann surfaces
• Two loop superstring amplitudes and S_6 representations
• Genus four superstring measures
• Lattice Theta Constants vs Riemann Theta Constants and NSR Superstring Measures
• More on superstring chiral measures
• The superstring cosmological constant and the Schottky form in genus 5

Cited by in corpus (8)

• One-Dimensional Super Calabi-Yau Manifolds and their Mirrors
• More on superstring chiral measures
• Extending the Belavin-Knizhnik "wonderful formula" by the characterization of the Jacobian
• Modular Invariant Regularization of String Determinants and the Serre GAGA Principle
• Finite Strings From Non-Chiral Mumford Forms
• Uniformization, Unipotent Flows and the Riemann Hypothesis
• Singular Spin Structures and Superstrings
• Eluding SUSY at every genus on stable closed string vacua