Warped compactification on curved manifolds

Understand

The characterization of a six- (or seven)-dimensional internal manifold with metric as having positive, zero or negative curvature is expected to be an important aspect of warped compactifications in supergravity.

• In this context, Douglas and Kallosh recently pointed out that a compact internal space with negative curvature could help to construct four-dimensional de Sitter solutions only if the extra dimensions are strongly warped or there are large stringy corrections.
• That is, the problem of finding 4-dimensional de Sitter solutions is well posed, if all extra dimensions are physically compact, which is called a no-go theorem.
• Here, we show that the above conclusion does not extend to a general class of warped compactifications in classical supergravity that allow a non-compact direction or cosmological solutions for which the internal space is asymptotic to a cone over a product of compact Einstein spaces or spheres.