Abstract
We apply the techniques of special Kähler geometry to investigate AdS4 vacua of general \( \mathcal{N} \) = 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 \( {\mathcal{P}_x} \) and their special Kähler covariant derivatives only, in a form that recalls the potential and the attractor equations of \( \mathcal{N} \) = 2 black holes. We propose a system of first order equations for the \( {\mathcal{P}_x} \) which generalize the supersymmetry conditions and yield nonsupersymmetric vacua. Special geometry allows us to recast these equations in algebraic form, and we find an infinite class of new \( \mathcal{N} \) = 0 and \( \mathcal{N} \) = 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.
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Cassani, D., Ferrara, S., Marrani, A. et al. A special road to AdS vacua. J. High Energ. Phys. 2010, 27 (2010). https://doi.org/10.1007/JHEP02(2010)027
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DOI: https://doi.org/10.1007/JHEP02(2010)027