Mapping Flux to Geometry
D3/D7-type flux compactifications are an exciting arena in which we have begun to address important problems in string theory and its applications to cosmology and particle physics – notably moduli stabilization, vacuum statistics, realizations of de Sitter space and inflation, and soft supersymmetry breaking in MSSM-like models. Given their relevance, we would like to understand which warped compactifications represent new string string vacua, and which are just alternative descriptions of more conventional fluxless compactifications. In this talk, we take a first step toward this larger goal in the friendlier confines of N = 2 supersymmetry. We study a duality that relates the simplest N = 2 warped compactifications to standard fluxless Calabi-Yau compactifications of type IIA string theory. Using the duality map, we show that the Calabi-Yau manifolds that arise are abelian surface (T4) fibrations over P1. We compute a variety of properties of these threefolds, including Hodge numbers, intersection numbers, discrete isometries, and H1(X, Z). In addition, we show that S-duality in the orientifold description becomes T-duality of the abelian surface fibers in the dual Calabi-Yau description.