Microscopic realization of the Kerr/CFT correspondence
Monica Guica
1
Andrew Strominger
0
Open Access
0
Center for the Fundamental Laws of Nature, Jefferson Physical Laboratory, Harvard University
,
Cambridge, MA 02138, U.S.A
1
Institut de Physique Theorique
, CEA Saclay, CNRS-URA 2306, 91191 Gif sur Yvette,
France
Supersymmetric M/string compactifications to five dimensions contain BPS black string solutions with magnetic graviphoton charge P and near-horizon geometries which are quotients of AdS3 S2. The holographic duals are typically known 2D CFTs with central charges cL = cR = 6P 3 for large P . These same 5D compactifications also contain non-BPS but extreme Kerr-Newman black hole solutions with SU(2)L spin JL and electric graviphoton charge Q obeying Q3 JL2 . It is shown that in the maximally charged limit Q3 JL2 , the near-horizon geometry coincides precisely with the right-moving temperature TR = 0 limit of the black string with magnetic charge P = JL1/3. The known dual of the latter is identified as the cL = cR = 6JL CFT predicted by the Kerr/CFT correspondence. Moreover, at linear order away from maximality, one finds a TR 6= 0 quotient of the AdS3 factor of the black string solution and the associated thermal CFT entropy reproduces the linearly sub-maximal Kerr-Newman entropy. Beyond linear order, for general Q3 < JL2 , one has a finite-temperature quotient of a warped deformation of the magnetic string geometry. The corresponding dual deformation of the magnetic string CFT potentially supplies, for the general case, the cL = cR = 6JL CFT predicted by Kerr/CFT. ArXiv ePrint: 1009.5039
Contents
1 Introduction 2 3 4
The conjecture
3.1 Full solution
3.2 Six-dimensional lift
3.3 Extremality
3.4 Near-horizon limit
The asymptotic symmetry group
5.1 The maximal case
5.2 Explicit brane construction
5.3 Linear deformations
5.4 Finite deformations A Long vs. short string pictures
Introduction
A complete accounting of the quantum microstates of a black hole requires a complete
quantum theory of gravity. Such a complete accounting was obtained for certain
supersymmetric black holes [1] by using string theory to identify their microstates with those
of a dual two-dimensional conformal field theory (2D CFT). Later it was realized [2] that
notable features of the construction in particular, matching the universality of the 2D
CFT Cardy formula to the universality of the Bekenstein-Hawking area law followed
largely from a careful analysis [3] of the properties of the diffeomorphism group in the AdS3
region near the horizon. This implies that the leading order agreement of the microscopic
and macroscopic pictures does not require any fine details of string theory. Rather, it must
follow a similar pattern for black holes with AdS3 near-horizon regions in any consistent
ultraviolet completion of quantum gravity.1 This is of course in accord with the expectation
that universal long-distance phenomena should not depend on the details of short-distance
microphysics. It has nevertheless been essential to our understanding to have the specific
microscopic examples in string theory [1] in which the general arguments of [2] are given a
concrete and fully self-consistent realization.
1Of course it is a logical possibility that string theory is the only such completion.
Recently, a general analysis of the near-horizon diffeomorphisms of astrophysical Kerr
black holes with near-maximal spins, patterned after [2, 3], has similarly indicated that they
are dual to 2D CFTs [4], but so far there has been no proposed string theoretic realization of
the duality. Evidence for the conjectured Kerr/CFT correspondence is given by the
agreement of the Cardy formula with the area law, the CFT correlators with near-superradiant
Press-Teukolsky greybody factors [58], and many other analyses [933]. However, there
are several puzzling features2 which are hard to understand without a concrete microscopic
construction. It is the purpose of this paper to fill this gap by proposing such a construction
for the general extreme five-dimensional Kerr-Newman black hole embedded as a solution
of string theory.
The basic idea is as follows. Supersymmetric M/string compactifications to five
dimensions have BPS string solutions with magnetic graviphoton charge P and a near-horizon
AdS3 S2 geometry. Typically, the dual CFT is explicitly known from a brane construction
and has central charges cL = cR = 6P 3 for large P . We will refer to it as the P 3 CFT.
For the special case of M-theory on a Calabi-Yau, the P 3 CFT is the worldvolume theory
of an M5-brane wrapping the 4-cycle associated to P , and is often referred to as the MSW
CFT [34]. We shall be primarily interested in the case where the Calabi-Yau contains a
torus factor and there is an uplift from five to six dimensions using the graviphoton fiber.
The total space of the graviphoton fiber over the near-horizon AdS3 S2 geometry is then
a quotient of AdS3 S3 [35, 36].
The same compactifications also contain non-supersymmetric (...truncated)