On Brane Back-Reaction and de Sitter Solutions in Higher-Dimensional Supergravity

TL;DR

This paper investigates how back-reaction of localized sources in higher-dimensional supergravity influences the lower-dimensional curvature, revealing conditions under which de Sitter solutions can exist despite no-go theorems.

Contribution

It derives an exact relation between lower-dimensional curvature and bulk field asymptotics, clarifies the role of sources in de Sitter solutions, and extends no-go theorem analyses to warped compactifications.

Findings

Back-reaction effects can cancel contributions that favor anti-de Sitter geometries.

Explicit 4D de Sitter solutions evade no-go theorems due to specific source contributions.

All classical Type IIB compactifications to 8D with only metric and axio-dilaton are 8D-flat.

Abstract

We argue that the problem of finding lower-dimensional de Sitter solutions to the classical field equations of higher-dimensional supergravity necessarily requires understanding the back-reaction of whatever localized objects source the bulk fields. However, we also find that most of the details of the back-reacted solutions are not important for determining the lower-dimensional curvature. We find, in particular, a classically exact expression that, for a broad class of geometries, directly relates the curvature of the lower-dimensional geometry to asymptotic properties of various bulk fields near the sources. Specializing to codimension-two sources, we find that the contribution involving the asymptotic behaviour of the warp factor (which has a definite sign for most supergravities and so is usually used to infer a preference for anti-de Sitter geometries) is precisely canceled by the contribution of the sources themselves (that are left out in earlier treatments). We identify which combination of bulk fields survives this cancelation, and so controls the sign of the lower-dimensional geometry, for several supergravities in 6, 10 and 11 dimensions. Our results show precisely why explicit 4D de Sitter solutions to 6D supergravity evade general no-go theorems. As an application we show that all classical compactifications of Type IIB supergravity (and F-theory) to 8 dimensions are 8D-flat if they involve only the metric and the axio-dilaton sourced by codimension-two sources, extending earlier results to include warped solutions and more general source properties.