Supersymmetric AdS vacua and separation of scales

TL;DR

This paper investigates supersymmetric massive IIA AdS4xS2(B4) vacua, revealing an attractor mechanism that enforces scale equality and showing that these vacua generally lack scale separation, with implications for their internal and external curvature ratios.

Contribution

It demonstrates that geometric moduli in these vacua are flux-quantization invariant and uncovers an attractor behavior leading to equal internal and external scales.

Findings

All sizes flow to equality near spacetime independently of initial conditions.

The KK spectrum is governed by a scale of the order of the AdS4 radius.

Curvature ratios are of order one, indicating no scale separation.

Abstract

The moduli space of the supersymmetric massive IIA AdS4xS2(B4) vacua, where S2(B4) is a two-sphere bundle over a four-dimensional Kaehler-Einstein base B4, includes three independent parameters which can be thought of as corresponding to the sizes of AdS4, B4 and the S2 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 AdS4 radius. Furthermore we point out that the curvature ratio in supersymmetric IIA AdS4 vacua with rigid SU(3) structure is of order one, indicating the absence of scale separation in this large class of vacua.