Spinning deformations of the D1-D5 system and a geometric resolution of Closed Timelike Curves

The SO(4) isometry of the extreme Reissner-Nordstrom black hole of N = 1, D = 5 supergravity can be partly broken, without breaking any supersymmetry, in two different ways. The “right” solution is a rotating black hole (BMPV); the “left” is interpreted as a black hole in a Gödel universe (GBH). In ten dimensions, both spacetimes are described by deformations of the D1-D5-pp-wave system with the property that the non-trivial Closed Timelike Curves (CTC’s) of the five dimensional manifold are absent in the universal covering space of the ten dimensional manifold. In the decoupling limit, the BMPV deformation is normalizable. It corresponds to the vev of an IR relevant operator of dimension ∆ = 1. The Gödel deformation is sub-leading in α unless we take an infinite vorticity limit; in such case it is a non-normalizable perturbation. It corresponds to the insertion of a vector operator of dimension ∆ = 5. Thus we conclude that from the dual (1+1)-CFT viewpoint the SO(4) R-symmetry is broken ‘spontaneously’ in the BMPV case and explicitly in the Gödel case.