T-duality of D-brane action at order α' in bosonic string theory

In bosonic string theory, it is known that the Buscher rules for the T-duality transformations receive quantum corrections at order $\alpha'$. In this paper, we use the consistency of the gravity couplings on the D-brane effective action at order $\alpha'$, with the above T-duality transformations to find the B-field and the dilaton couplings. We show that these couplings are fully consistent with the corresponding disk-level S-matrix elements in string theory.