S-Duality, SL(2,Z) Multiplets and Killing Spinors

The S-duality transformations in type IIB string theory can be seen as local U(1) transformations in type IIB supergravity. We use this approach to construct the $SL(2,Z)$ multiplets associated to supersymmetric backgrounds of type IIB string theory and the transformation laws of their corresponding Killing spinors.