Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-10-04
JHEP 9810 (1998) 015
Physics
High Energy Physics
High Energy Physics - Theory
12 pages, LaTex2e
Scientific paper
10.1088/1126-6708/1998/10/015
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, thereby verifying the $SL(2,Z)$ invariance of the D3-brane action in the $AdS_5 \times S^5$ background as in the flat background. To this end, we fix the $\kappa$-symmetry in a gauge which simplifies the classical action in order to perform an SO(2) rotation of the N=2 spinor index in a manifest way, though this may not be necessary. This situation is the same as the case of a super D-string on $AdS_5 \times S^5$ where it was shown that the super D-string action is transformed to a form of the IIB Green-Schwarz superstring action with the $SL(2,Z)$ covariant tension in the $AdS_5 \times S^5$ background through a duality transformation. These results strongly suggest that various duality relations originally found in the flat background may be independent of background geometry, in other words, the duality transformations in string and p-brane theories may exist even in general curved space-time.
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