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Summarizing the results of [1], we discuss the four‐dimensional effective approach to type II N = 1 supersymmetric flux compactifications with general SU(3) × SU(3)‐structure. In particular, we study the effect of a non‐trivial warp factor, which we argue leads naturally to a supergravity formulation invariant under local complexified Weyl transformations. We show that the full ten‐dimensional supersymmetry equations can be obtained as F‐flatness and D‐flatness conditions from the superpotential and Kähler potential. We then consider non‐perturbative corrections to these supersymmetry conditions, following from adding instanton or gaugino condensation effects to the superpotential. As examples, we show how smeared instantons allow to understand the ten‐dimensional geometry of KKLT‐like AdS vacua and we give an explanation for the superpotential for “mobile” D3‐branes in terms of a non‐perturbatively induced generalized complex structure.

Warped generalized geometry compactifications, effective theories and non‐perturbative effects