Recently, it has been observed that in a T-duality invariant world-volume theory in at spacetime, all orders of gauge field strength and all orders of the D-brane velocity appear in two specific matrices. Using these two matrices, we construct the worldvolume couplings of two massless NSNS states at order a’2 and all orders of the velocity and the gauge field strength, by requiring them to be invariant under the linear T-duality. The standard extension F -> F +P[B], then produces all orders of the pull-back of B-_field into the action. We compare the resulting couplings for zero velocity and gauge field strength, with the a’2 terms of the disk-level S-matrix element of two massless NSNS vertex operators in the presence of a constant background B-field. We have found an exact agreement.

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