Remarks on Superstring amplitudes in higher genus

TL;DR

This paper discusses recent progress in understanding superstring amplitudes at higher genus, focusing on Grushevsky's modular form approach and conjectures for the superstring measure.

Contribution

It provides evidence supporting Grushevsky's ansatz and conjectures for the superstring measure in higher genus, advancing the theoretical framework.

Findings

Supports the validity of Grushevsky's approach

Provides evidence for the conjectured superstring measure formula

Highlights the importance of modular forms with holomorphic roots

Abstract

Very recently, Grushevsky continued D'Hoker and Phong's program of finding the chiral superstring measure from first principles by constructing modular forms satisfying certain factorization constraints. He has proposed an ansatz in genus 4 and conjectured a possible formula for the superstring measure in any genus, subject to the condition that certain modular forms admit holomorphic roots. In this note we want to give some evidence that Grushevsky's approach seems to be very fruitful.