Supersymmetric 3D anti-de Sitter space solutions of type IIB supergravity

For every positively curved Kähler-Einstein manifold in four dimensions, we construct an infinite family of supersymmetric solutions of type IIB supergravity. The solutions are warped products of AdS3 with a compact seven-dimensional manifold and have nonvanishing five-form flux. Via the anti-de Sitter/conformal field theory correspondence, the solutions are dual to two-dimensional conformal field theories with (0,2) supersymmetry. The corresponding central charges are rational numbers.

Gödel's universe in a Supertube shroud

We demonstrate that certain supersymmetric Gödel-like universe solutions of supergravity are not solutions of string theory. This is achieved by realizing that supertubes are Bogomol'nyi-Prasad-Sommerfeld states in these spaces, and under certain conditions, when wrapping closed timelike curves, some world-volume modes develop negative kinetic terms. Since these universes are homogeneous, this instability takes place everywhere in space-time. We also construct a family of supergravity solutions which locally look like the Gödel universe inside a domain wall made out of supertubes, but have very different asymptotic structure. One can adjust the volume inside the domain wall so there will be no closed timelike curves, and then those spaces seem like perfectly good string backgrounds.