The closed-string 3-loop amplitude and S-duality

TL;DR

This paper computes the low-energy limit of the four-point 3-loop amplitude in type IIA and IIB superstring theories using pure spinor formalism, confirming S-duality predictions for the type IIB $D^6 R^4$ interaction.

Contribution

It provides the first explicit calculation of the 3-loop amplitude's low-energy limit in both superstring theories, validating S-duality predictions.

Findings

Agreement with S-duality predictions for type IIB $D^6 R^4$ interaction

Explicit 3-loop amplitude calculation in pure spinor formalism

Confirmation of theoretical predictions for superstring interactions

Abstract

The low-energy limit of the four-point 3-loop amplitude (including its overall coefficient) is computed in both type IIA and IIB superstring theories using the pure spinor formalism. The result is shown to agree with the prediction of the coefficient for the type IIB $D^6 R^4$ interaction made by Green and Vanhove based on S-duality considerations.