SL(2,Z) S-duality of Super D-string Action in Type IIB Supergravity Background

It is shown in a quantum-mechanically exact manner that a supersymmetric and $\kappa$-symmetric D-string action in a general type IIB supergravity background is transformed to a form of the type IIB Green-Schwarz superstring action with the SL(2,Z) covariant tension through an S-duality transformation. This result precisely proves a conjecture mentioned previously that the SL(2,Z) S-duality of a super D-string action in a flat background is also valid even in a curved IIB background geometry. We point further out the validity of the more generalized conjecture that various duality relations of super D-brane and M-brane actions originally found in a flat background also hold true in general ten dimensional type II supergravity and eleven dimensional supergravity background geometries by applying the present formalism to those cases.