Komeil Babaei Velni, Mohammad R. Garousi
Recently it has been speculated that the S-matrix elements satisfy the Ward identity associated with the T-duality. This indicates that a group of S-matrix elements are invariant under the linear T-duality transformations on the external states. If one evaluates one component of such T-dual multiplet, then all other components may be found by the simple use of the linear T-duality transformations. The assumption implicit in the T-duality transformations that fields must be independent of the coordinate along which the T-duality imposed, however, may cause the T-dual multiplet not to be complete. The missing part, on the other hand, may be found by imposing the Ward identity associated with the gauge transformations. In this paper, we apply the T-dual Ward identity on the disk-level S-matrix element of one RR $(p-3)$-form with one transverse index, and two arbitrary NSNS states on the world volume of a D$_p$-brane and find its corresponding T-dual multiplet. %This multiplet has five components which includes the S-matrix element of the RR $(p-1)$-form, $(p+1)$-form, ($p+3)$-form, $(p+5)$-form as well as the original $(p-3)$-form. This multiplet, however, is not complete. Imposing the Ward identity associated with the gauge transformations, we find the missing pieces. We show that the multiplet is reproduced by explicit calculation, and its low energy contact terms at order $\alpha'^2$ are consistent with the existing couplings in the literature.
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http://arxiv.org/abs/1204.4978
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