Abstract: Recently, it has been found that there are couplings of the RR field strength F(p) and the B-field strength H on the world volume of Dp-branes at order O(α′2). These couplings which have both world-volume and transverse indices, are invariant under the linear T-duality transformations. Consistency with the nonlinear T-duality indicates that the RR field strength F(p) in these couplings should be replaced by F(p) = dC(p−1) where C = eBC. This replacement, however, produces some non-gauge invariant terms. On the other hand, the nonlinear terms are invariant under the linear T-duality transformations at the level of two B-fields. This allows one to remove some of the nonlinear terms in F(p). We fix this by comparing the nonlinear couplings with the S-matrix element of one RR and two NSNS vertex operators. Our results indicate that in the expansion of F(p) one should keep only the B-field gauge invariant terms, e.g., B ∧ dC(p−3) where both indices of B-field lie along the brane. Moreover, in this case one should replace B with B + 2πα′f to have the B-field gauge invariance.

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