NSR superstring measures in genus 5

TL;DR

This paper investigates superstring measure ansatze in genus 5, demonstrating their differences, proposing a new combined ansatz that satisfies certain amplitude properties, and discussing limitations in genus 6 constructions.

Contribution

It shows the non-coincidence of Grushevsky and OPSMY ansatze in genus five and proposes a new combined ansatz that satisfies superstring amplitude properties.

Findings

Grushevsky and OPSMY ansatze differ in genus five.

A new combined ansatz satisfies the vanishing two-point function in genus four.

No suitable ansatz exists for genus six with current known forms.

Abstract

Currently there are two proposed ansatze for NSR superstring measures: the Grushevsky ansatz and the OPSMY ansatz, which for genera g<=4 are known to coincide. However, neither the Grushevsky nor the OPSMY ansatz leads to a vanishing two point function in genus four, which can be constructed from the genus five expressions for the respective ansatze. This is inconsistent with the known properties of superstring amplitudes. In the present paper we show that the Grushevsky and OPSMY ansatze do not coincide in genus five. Then, by combining these ansatze, we propose a new ansatz for genus five, which now leads to a vanishing two-point function in genus four. We also show that one cannot construct an ansatz from the currently known forms in genus 6 that satisfies all known requirements for superstring measures.