Generalized non-supersymmetric flux vacua

We discuss a novel strategy to construct 4D = 0 stable flux vacua of type II string theory, based on the existence of BPS bounds for probe D-branes in some of these backgrounds. In particular, we consider compactifications where D-branes filling the 4D space-time obey the same BPS bound as they would in an = 1 compactification, while other D-branes, like those appearing as domain walls from the 4D perspective, can no longer be BPS. We construct a subfamily of such backgrounds giving rise to 4D = 0 Minkowski no-scale vacua, generalizing the well-known case of type IIB on a warped Calabi-Yau. We provide several explicit examples of these constructions, and compute quantities of phenomenological interest like flux-induced soft terms on D-branes. Our results have a natural, simple description in the language of Generalized Complex Geometry, and in particular in terms of D-brane generalized calibrations. Finally, we extend the integrability theorems for 10D supersymmetric type II background...