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

TL;DR

This paper explores deformations of the D1-D5 system that resolve closed timelike curves, analyzing their properties and implications for dual conformal field theories, with a focus on supersymmetry and geometric regularization.

Contribution

It introduces specific spinning deformations of the D1-D5 system that eliminate closed timelike curves and examines their dual CFT interpretations, highlighting differences between BMPV and Godel cases.

Findings

BMPV deformation is normalizable and corresponds to a relevant operator.

Godel deformation is non-normalizable unless vorticity is infinite.

SO(4) R-symmetry is broken spontaneously in BMPV and explicitly in Godel.

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 Godel universe. 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 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 \Delta=1. The Godel deformation is sub-leading in \alpha' 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 \Delta=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 Godel case.