Sl(2,R)-Duality Covariance of Killing Spinors in Axion-Dilaton Black Holes

Under $SL(2,R)$ electric-magnetic duality transformations the Bogomolnyi bound of dilaton-axion black holes is known to be invariant. In this paper we show that this invariance corresponds to the covariance of the $N=4$ supersymmetry transformation rules and their parameters. In particular this implies that Killing spinors transform covariantly into Killing spinors. As an example, we work out completely the case of the largest known family of axion-dilaton black holes which is $SL(2,R)$-invariant, finding the Killing spinors with the announced properties.