α′-Corrections to DBI action via T-duality constraint

It is known that Dp-brane effective action at the leading order of α′ in flat space–time which is given by DBI action, transforms to Dp−1-brane effective action under standard T-duality transformations of the open string gauge bosons and transverse scalar fields. Extending this duality to order α′, one may find corrections to the DBI action which include the second fundamental form Ω and the covariant derivative of gauge field strength DF, as well as the corrections to the T-duality transformations. Using this idea, up to two parameters, we have found all 81 covariant couplings of DFDF and ΩΩ with zero, two, four and six F's. The four gauge field couplings that the T-duality constraint fixes are consistent with the known couplings in the literature