Three-forms in supergravity and flux compactifications

We present a duality procedure that relates conventional four-dimensional matter-coupled N = 1 super-gravities to dual formulations in which auxiliary fields are replaced by field strengths of gauge three-forms. The duality promotes specific coupling constants appearing in the super-potential to vacuum expectation values of the field strengths. We then apply this general duality to type IIA string compact-ifications on Calabi-Yau orientifolds with RR fluxes. This gives a new supersymmetric formulation of the corresponding effective four-dimensional theories which includes gauge three-forms.