Higher genus superstring amplitudes from the geometry of moduli spaces

TL;DR

This paper demonstrates how the geometry of moduli space of Riemann surfaces constrains higher genus superstring amplitudes, proposing a natural formula based on recent geometric and combinatorial insights.

Contribution

It introduces a new approach to compute higher genus superstring amplitudes using the geometry of moduli space and determinants of holomorphic differentials.

Findings

The proposed amplitude formula satisfies key geometric and physical conditions.

The approach leverages the Siegel induced metric on moduli space.

Results connect superstring amplitudes with complex geometry of Riemann surfaces.

Abstract

We show that the higher genus 4-point superstring amplitude is strongly constrained by the geometry of moduli space of Riemann surfaces. A detailed analysis leads to a natural proposal which satisfies several conditions. The result is based on the recently derived Siegel induced metric on the moduli space of Riemann surfaces and on combinatorial products of determinants of holomorphic abelian differentials.