Superstring measure and non-renormalization of the three-point amplitude

TL;DR

This paper investigates the superstring three-point amplitude at three-loop order, revealing potential deviations from non-renormalization theorems and proposing a correction that could restore expected vanishing behavior.

Contribution

It identifies a failure in the conjectured superstring measure at three-loop and proposes a candidate correction to reconcile with non-renormalization theorems.

Findings

Conjectured measure fails to vanish at three-loop

A candidate correction may restore non-renormalization

New identity supports the corrected amplitude vanishing

Abstract

We show that a recently conjectured expression for the superstring three-point amplitude, in the framework of the Cacciatori, Dalla Piazza, van Geemen - Grushevsky ansatz for the chiral measure, fails to vanish at three-loop, in contrast with expectations from non-renormalization theorems. Based on analogous two-loop computations, we discuss the possibility of a non-trivial correction to the amplitude and propose a natural candidate for such a contribution. Thanks to a new remarkable identity, it is reasonable to expect that the corrected three-point amplitude vanishes at three-loop, recovering the agreement with non-renormalization theorems.