AdS${}_2$ Type-IIA Solutions and Scale Separation

Abstract

In this note we examine certain classes of solutions of IIA theory without sources, of the form AdS${}_2\times {\mathcal{M}}^{(1)}\times \cdots \times {\mathcal{M}}^{(n)}$, where ${\mathcal{M}}^{(i)}$ are Riemannian spaces. We show that large hierarchies of curvatures can be obtained between the different factors, however the absolute value of the scalar curvature of AdS${}_2$ must be of the same order or larger than the absolute values of the scalar curvatures of all the other factors.

20 pages, one additional ref. in replaced version, 2nd replaced version with minor corrections