[ensl-00432620, v1] A special road to AdS vacua

We apply the techniques of special Kähler geometry to investigate AdS4 vacua of general N = 2 gauged supergravities underlying flux compactifications of type II theories. We formulate the scalar potential and its extremization conditions in terms of a triplet of prepotentials Px and their special Kähler covariant derivatives only, in a form that recalls the potential and the attractor equations of N = 2 black holes. We propose a system of first order equations for the Px which generalize the supersymmetry conditions and yield non-supersymmetric vacua. Special geometry allows us to recast these equations in algebraic form, and we find an infinite class of new N = 0 and N = 1 AdS4 solutions, displaying a rich pattern of non-trivial charges associated with NSNS and RR fluxes. Finally, by explicit evaluation of the entropy function on the solutions, we derive a U-duality invariant expression for the cosmological constant and the central charges of the dual CFT’s. en sl -0 04 32 62 0, v er si on 1 16 N ov 2 00 9