On the supergravity formulation of mirror symmetry in generalized Calabi-Yau manifolds.

We derive the complete supergravity description of the N = 2 scalar potential which realizes a generic flux-compactification on a Calabi-Yau manifold (generalized geometry). The effective potential Veff = V(@ZV =0), obtained by integrating out the massive axionic fields of the special quaternionic manifold, is manifestly mirror symmetric, i.e. invariant with respect to Sp(2 h2 + 2) × Sp(2 h1 + 2) and their exchange, being h1, h2 the complex dimensions of the underlying special geometries. Veff has a manifestly N = 1 form in terms of a mirror symmetric superpotential W proposed, some time ago, by Berglund and Mayr.