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-Infeld and Chern-Simons actions, 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 2-form and the $S$-matrix element of six gauge bosons in favor of the above proposal.

• Received 5 May 2013

DOI:https://doi.org/10.1103/PhysRevD.88.026008