Thurston Geometries from Eleven Dimensions

In three dimensions, a `master theory' for all Thurston geometries requires imaginary flux. However, these geometries can be obtained from physical three-dimensional theories with various additional scalar fields, which can be interpreted as moduli in various compactifications of a higher-dimensional `master theory'. Three Thurston geometries are of the form N_2 x S^1, where N_2 denotes a two-dimensional Riemannian space of constant curvature. This enables us to twist these spaces, via T-duality, into other Thurston geometries as a U(1) bundle over N_2. In this way, Hopf T-duality relates all but one of the geometries in the higher-dimensional M-theoretic framework. The exception is the `Sol geometry,' which results from the dimensional reduction of the decoupling limit of the D3-brane in a background B-field.Comment: Latex, 8 pages, improved presentation in abstract, introduction and section 2, references adde

Phases of Braneworlds, Spinning D3-branes and Strongly-Coupled Gauge Theories

A spinning nonextremal D3-brane undergoes a phase transition to a naked singularity which, from the braneworld point of view, corresponds to the apparent graviton speed passing from subluminal to superluminal. We investigate this phase transition from the dual perspectives of braneworld scenarios and holography. We discuss the relevance of the thermodynamic stability domains of a spinning D3-brane to the physics of braneworld scenarios. We also describe various gravitational Lorentz violations which arise from static D3-branes.Comment: 18 pages, 6 figures, LaTeX, additional comment and reference

From de Sitter to de Sitter

We obtain D=6, N=(1,1) de Sitter supergravity from a hyperbolic reduction of the massive type IIA* theory. We construct a smooth cosmological solution in which the co-moving time runs from an infinite past, which is dS_4\times S^2, to an infinite future, which is a dS_6-type spacetime with the boundary R^3\times S^2. This provides an effective four-dimensional cosmological model with two compact extra dimensions forming an S^2. Interestingly enough, although the solution is time-dependent, it arises from a first-order system via a superpotential construction. We lift the solutions back to D=10, and in particular obtain two smooth embeddings of dS_4 in massive type IIA*, with the internal space being either H^4\times S^2 or an H^4 bundle over S^2. We also obtain the analogous D=5 and D=4 solutions. We show that there exist cosmological solutions that describe an expanding universe with the expansion rate significantly larger in the past than in the future.Comment: Latex three times, 22 pages, references adde