Remarks on scale separation in flux vacua

Abstract

We argue that the Maldacena-Nuñez no-go theorem excluding Minkowski and de Sitter vacua in flux compactifications can be extended to anti-de Sitter (AdS) vacua for which the Kaluza-Klein scale is parametrically smaller than the AdS length scale. In the absence of negative tension sources, scale-separated AdS vacua are ruled out in 11-dimensional supergravity; in 10-dimensional supergravity, we show that such vacua can only arise in conjunction with large dilaton gradients. As a practical application of this observation we demonstrate that the mechanism to resolve O6 singularities in massive type IIA at the classical level is likely not to occur in AdS compactifications with scale separation. We furthermore remark that a compactification to four observable dimensions implies a large cosmological hierarchy.

Open Problems on Classical de Sitter Solutions

“…While the equations derived here agree with those of [] (for instance for , we get as there), the interpretation of the result differs. We consider here that the separation of scale should be defined by a large hierarchy between the 4d scale and the internal typical scale L , defined e.g.…”

“…by the volume; we have in mind that the internal Kaluza–Klein energy scale, defined by the (square root of the) first eigenvalue of the Laplacian on scalar fields, should be close to . On the contrary, the internal scale compared to the 4d scale in [] is defined by the average of ; the authors also specify that if this scale is different than the Kaluza–Klein scale, their analysis does not apply. We believe that for manifolds admitting the desired internal hierarchy, i.e.…”

O‐Plane Backreaction and Scale Separation in Type IIA Flux Vacua

“…• Another work studying the resolution of the O6-plane singularities is [15]. There, it was argued that AdS solutions of type II (or 11d) supergravity cannot have scale separation unless they have explicit O-plane sources or large integrated dilaton gradients.…”

“…11 Since the regular solution found in [11] has no explicit O-planes and an almost constant dilaton, [15] concluded that it cannot appear in vacua with scale separation such as the DGKT vacua. However, as we will discuss in more detail in Section 6, the argument of [15] is based on two assumptions about the KK scale which do not hold in general (and are indeed violated in the DGKT vacua). We therefore believe that the argument does not imply that a solution with resolved O-plane singularities would require large dilaton gradients.…”

“…Note that the earlier work [15] already derived a no-go theorem against scale separation for the case of AdS vacua without O-planes. However, as we will explain in more detail below, the bound derived there does actually not forbid AdS/KK scale separation in such vacua if the KK scale is small compared to the Planck scale (which should be the case in a controlled flux compactification).…”