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 V-eff = V(partial derivative(Z) V=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(2h(2) + 2) x Sp(2h(1) + 2) and their exchange, being h(1), h(2) the complex dimensions of the underlying special geometries. V-eff has a manifestly N = 1 form in terms of a mirror symmetric superpotential W proposed, some time ago, by Berglund and Mayr. (C) 2007 Elsevier B.V. All rights reserved.