S-duality of color-ordered amplitudes

TL;DR

This paper investigates the S-duality symmetry of color-ordered amplitudes involving multiple D3-branes, extending previous abelian results to nonabelian cases and confirming predictions through explicit calculations.

Contribution

It introduces the linear S-duality transformation for nonabelian gauge field commutators and applies S-duality to derive and verify nonabelian S-matrix elements.

Findings

S-matrix elements are consistent with S-dual Ward identities.

Derived the S-duality transformation of nonabelian gauge field commutators.

Explicit calculations confirm the S-duality predictions.

Abstract

Recently, it has been proposed that the S-matrix elements on the world volume of an abelian D$_3$-brane are consistent with the Ward identity associated with the S-duality. In this paper we extend this study to the case of multiple D$_3$-branes. We speculate that the S-matrix elements are consistent with the S-dual Ward identity irrespective of the ordering of the external states. Imposing this symmetry on the particular case of the S-matrix element of one Kalb-Ramond, one transverse scalar and two nonabelian gauge bosons, we will find the linear S-duality transformation of the commutator of two nonabelian gauge field strengths. Using this transformation and the standard S-duality transformations of the supergravity fields, all other nonabelian S-matrix elements of one closed and three open string states can be found by the S-duality proposal. We will show that the predicted S-matrix elements are reproduced exactly by explicit calculations.