T-duality of curvature terms in D-brane actions

We examine the known curvature terms in the DBI part of the D-brane action under the T-duality transformation. Using the compatibility of the action with the standard rules of T-duality at the linear order as a guiding principle, we include the appropriate NS-NS B-field terms in the action and show that they reproduce the O(alpha'(2)) terms of the corresponding disk-level scattering amplitude. Consistency with the T-duality transformations indicates that, apart from the overall factor of e(-phi), there may be no dilaton coupling in the string frame action. We check this by the scattering amplitude at order O(alpha'(2)).