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Electrified branes

A geometrical form of the supersymmetry conditions for D-branes on arbitrary type II supersymmetric backgrounds is derived, as well as the associated BPS bounds. The treatment is general and allows to consider, for instance, non-static configurations or D-branes supporting a non-vanishing electric flux, hence completing previous partial results. In particular, our discussion clarifies how the notion of calibration can be extended in order to be applicable to the most general supersymmetric configurations. As an exemplifying preliminary step, the procedure followed is first applied to fundamental strings.