S-duality of color-ordered amplitudes

Recently, it has been proposed that the S-matrix elements on the world volume of an abelian D₃-brane are consistent with the Ward identity associated with the S-duality. In this paper we extend this study to the case of multiple D₃-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 non-abelian gauge bosons, we will find the linear S-duality transformation of the commutator of two non-abelian gauge field strengths. Using this transformation and the standard S-duality transformations of the supergravity fields, all other non-abelian 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.