Genus four superstring measures
arXiv:0804.0457 · doi:10.1007/s11005-008-0260-9
Abstract
A main issue in superstring theory are the superstring measures. D'Hoker and Phong showed that for genus two these reduce to measures on the moduli space of curves which are determined by modular forms of weight eight and the bosonic measure. They also suggested a generalisation to higher genus. We showed that their approach works, with a minor modification, in genus three and we announced a positive result also in genus four. Here we give the modular form in genus four explicitly. Recently S. Grushevsky published this result as part of a more general approach.
7 pages. To appear in Letters in Mathematical Physics
References in corpus (6)
- Two-Loop Superstrings I, Main Formulas
- Two-Loop Superstrings IV, The Cosmological Constant and Modular Forms
- Modular Forms and Three Loop Superstring Amplitudes
- Asyzygies, modular forms, and the superstring measure II
- Superstring scattering amplitudes in higher genus
- Remarks on Superstring amplitudes in higher genus
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- The vanishing of two-point functions for three-loop superstring scattering amplitudes
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- One-Dimensional Super Calabi-Yau Manifolds and their Mirrors
- Classical theta constants vs. lattice theta series, and super string partition functions
- More on superstring chiral measures
- Extending the Belavin-Knizhnik "wonderful formula" by the characterization of the Jacobian
- NSR superstring measures in genus 5
- Equidistribution Rates, Closed String Amplitudes, and the Riemann Hypothesis
- Modular Invariant Regularization of String Determinants and the Serre GAGA Principle
- Boundary contributions to three loop superstring amplitudes
- Finite Strings From Non-Chiral Mumford Forms
- Calculation and modular properties of multi-loop superstring amplitudes
- Eluding SUSY at every genus on stable closed string vacua
- Singular Spin Structures and Superstrings