Duality of Super D-brane Actions in Type IIB Supergravity Background
  We show that supersymmetric and $\kappa$-symmetric Dp-brane actions in type II supergravity background have the same duality transformation properties as those in a flat Minkowskian background. Specially, it is shown that the super D-string transforms in a covariant way while the super D3-brane is self-dual under the $SL(2,Z)$ duality. Also, the D2-brane and the D4-brane transform in ways expected from the relation between type IIA superstring theory and M-theory. The present study proves that various duality symmetries, which were originally found in the flat background field, are precisely valid even in the curved background geometry. 
Tadahiko Kimura and Ichiro Oda