Spinning deformations of the D1–D5 system and a geometric resolution of closed timelike curves

Abstract

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 Δ=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 Δ=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.