A special road to AdS vacua

TL;DR

This paper uses special Kaehler geometry to analyze AdS_4 vacua in N=2 gauged supergravity, discovering new solutions and deriving U-duality invariant expressions for key physical quantities.

Contribution

It formulates the scalar potential and extremization conditions in terms of triplets of prepotentials, generalizing supersymmetry conditions to find new non-supersymmetric AdS_4 vacua.

Findings

Found an infinite class of new N=0 and N=1 AdS_4 solutions.

Recast equations in algebraic form using special geometry.

Derived a U-duality invariant expression for the cosmological constant and dual CFT central charges.

Abstract

We apply the techniques of special Kaehler geometry to investigate AdS_4 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 P_x and their special Kaehler 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 P_x 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 AdS_4 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.