S-duality of tree-level S-matrix elements in D$_3$-brane effective action

Recently it has been speculated that the S-matrix elements on the world volume of D$_3$-branes should satisfy the ward identity corresponding to the S-duality transformations. For a single brane and in the low energy limit, this indicates that in the abelian Dirac-Born-Indeld-Chern-Simons theory the combination of contact terms and tree-level massless poles in an $n$-point function should satisfy the S-duality. In this paper we examine in details the S-matrix element of three gauge bosons and one two-form and the S-matrix element of six gauge bosons in favor of the above proposal.