Supersymmetric AdS vacua and separation of scales

A bstract The moduli space of the supersymmetric massive IIA AdS 4 × S 2 (B 4 ) vacua, where S 2 (B 4 ) is a two-sphere bundle over a four-dimensional Kähler-Einstein base B 4 , includes three independent parameters which can be thought of as corresponding to the sizes of AdS 4 , B 4 and the S 2 fiber. It might therefore be expected that these vacua do not suffer from the absence of scale separation. We show that the independence of the geometric moduli survives flux quantization. However, we uncover an attractor behavior whereby all sizes flow to equality in some neighborhood of spacetime independently of the initial conditions set by the parameters of the solution. This is further confirmed by the study of the ratio of internal to external scalar curvatures. We also show that the asymptotic Kaluza-Klein spectrum of a ten-dimensional massive scalar is governed by a scale of the order of the AdS 4 radius. Furthermore we point out that the curvature ratio in supersymmetric IIA AdS 4 vacua with rigid SU(3) structure is of order one, indicating the absence of scale separation in this large class of vacua.