RNS superstring measure for genus 3

Abstract

We propose a new formula for the RNS supersting measure for genus 3. Our derivation is based on invariant theory. We follow Witten's idea of using an algebraic parametrization of the moduli space (which he applied to re-derive D'Hoker and Phong's formula for the RNS superstring measure for genus 2); but the particular parametrization that we use has not been applied to superstring theory before. We prove that the superstring measure is a linear combinaition (with complex coefficients) of three known functions. Furthermore, we conjecture the values of the coefficients of this linear combination and provide evidence for this conjecture. Unlike the Ansatz of Cacciatori, Dalla Piazza and van Geemen from 2008, our formula has a polar singularity along the hyperelliptic locus; the existence of this singularity was established by Witten in 2015. Moreover, our formula is not an Ansatz but follows from first principles, except for the values of the three coefficients.

54 pages. Added more details, most importantly on the 0-point function

References in corpus (15)

• The closed-string 3-loop amplitude and S-duality
• Two-Loop Superstrings IV, The Cosmological Constant and Modular Forms
• Quartic Curves and Their Bitangents
• 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
• Superstring loop amplitudes from the field theory limit
• The Super Period Matrix With Ramond Punctures
• NSR Superstring Measures Revisited
• Lattice Theta Constants vs Riemann Theta Constants and NSR Superstring Measures
• Integration on Non-Compact Supermanifolds
• Moduli and Periods of Supersymmetric Curves
• NSR superstring measures in genus 5
• Boundary contributions to three loop superstring amplitudes