Abstract :
The S-duality transformations of the lowest order string effective theory admit a space time interpretation for 4-dim backgrounds with one Killing symmetry. Starting from pure gravity and performing a sequence of interwined T-S-T duality transformations we obtain new solutions which are always purely gravitational. In this fashion, S-duality induces an SL(2,R) transformation in the space of target space metrics, which coincides with the action of the Ehlers-Geroch group and interchanges the electric with the magnetic aspects of gravity. Specializing to gravitational instanton backgrounds, we show that ALE instantons are mapped to (multi) Taub-NUT backgrounds and vice versa. We find, however, that the self-duality of the metric is not generically preserved, unless the corresponding Killing vector field has self-dual covariant derivatives. Thus, the T-S-T transformations are not always compatible with the world-sheet supersymmetry of N = 4 superconformal string vacua. We also provide an algebraic characterization of the corresponding obstruction and associate it with a breakdown of space time supersymmetry under rotational T-duality transformations.
