Asyzygies, modular forms, and the superstring measure I

TL;DR

This paper explores new formulas for the two-loop superstring chiral measure that can be extended to higher genus, aiming to find viable ansatze for the three-loop superstring measure.

Contribution

It introduces two alternative modular covariant formulas for the two-loop superstring chiral measure, with detailed analysis of one, facilitating higher genus generalizations.

Findings

Derived two alternative formulas for the two-loop superstring measure

One formula admits modular covariant generalization to higher genus

Provides groundwork for three-loop superstring measure ansatz

Abstract

The goal of this paper and of a subsequent continuation is to find some viable ansatze for the three-loop superstring chiral measure. For this, two alternative formulas are derived for the two-loop superstring chiral measure. Unlike the original formula, both alternates admit modular covariant generalizations to higher genus. One of these two generalizations is analyzed in detail in the present paper, with the analysis of the other left to the next paper of the series.