SL(2,Z) self-duality of super D3-brane action on AdS5 × S5

It is shown that a supersymmetric and $\kappa$-symmetric D3-brane action on$AdS_5 \times S^5$ is mapped into itself by a duality transformaion, therebyverifying the $SL(2,Z)$ invariance of the D3-brane action in the $AdS_5 \timesS^5$ background as in the flat background. To this end, we fix the$\kappa$-symmetry in a gauge which simplifies the classical action in order toperform an SO(2) rotation of the N=2 spinor index in a manifest way, thoughthis may not be necessary. This situation is the same as the case of a superD-string on $AdS_5 \times S^5$ where it was shown that the super D-stringaction is transformed to a form of the IIB Green-Schwarz superstring actionwith the $SL(2,Z)$ covariant tension in the $AdS_5 \times S^5$ backgroundthrough a duality transformation. These results strongly suggest that variousduality relations originally found in the flat background may be independent ofbackground geometry, in other words, the duality transformations in string andp-brane theories may exist even in general curved space-time.Comment: 12 pages, LaTex2