D-brane Construction of the 5D NHEK Dual

Extremal but non-supersymmetric charged black holes with SU(2)_L spin in IIB string theory compactified to five dimensions on K^3 x S^1 are considered. These have a near-horizon or NHEK region with an enhanced SL(2,R)_L conformal symmetry. It is shown that the NHEK geometry has a second, inequivalent, asymptotically flat extension in which the radius of the S^1 becomes infinite but the radius of the angular circles of SU(2)_L orbits approach a constant. The asymptotic charges associated to the second solution identify it as a 5D D1-D5-Taub-NUT black string with certain nonzero worldvolume charge densities, temperatures and chemical potentials. The dual of the NHEK geometry is then identified as an IR limit of this wrapped brane configuration.Comment: 11 page

On R**2 Corrections for 5D Black Holes

We study higher order corrections to extremal black holes/black string in five dimensions. These higher order corrections are due to supersymmetric completion of R**2 term in five dimensions. By making use of the results we extend the notion of very special geometry when higher derivative terms are also taken into account. This can be used to make a connection between total bundle space of near horizon wrapped M2's and wrapped M5's in the presence of higher order corrections. We also show how the corrected geometry removes the singularity of a small black hole.Comment: 16 pages, latex file, V3: typos corrected, refs added, V4; minor corrections, few comments added, refs adde

Central Charge for AdS_2 Quantum Gravity

Two-dimensional Maxwell-dilaton quantum gravity on AdS_2 with radius $\ell$ and a constant electric field E is studied. In conformal gauge, this is equivalent to a CFT on a strip. In order to maintain consistent boundary conditions, the usual conformal diffeomorphisms must be accompanied by a certain U(1) gauge transformation. The resulting conformal transformations are generated by a twisted stress tensor, which has a central charge $c={3k E^2 \ell^4/4}$ where k is the level of the U(1) current. This is an AdS_2 analog of the Brown-Henneaux formula $c = 3\ell/2G$ for the central charge of quantum gravity on AdS_3

Kerr/CFT Correspondence in the Low Energy Limit of Heterotic String Theory

We investigate the recently proposed Kerr/CFT correspondence in the context of heterotic string theory. The Kerr/CFT correspondence states that the near-horizon states of an extremal four (or higher) dimensional black hole could be identified with a certain chiral conformal field theory under the conjecture that the central charges from the non-gravitational fields vanish. The corresponding Virasoro algebra is generated by a class of diffeomorphisms which preserves the appropriate boundary conditions on the near-horizon geometry. To understand the chiral conformal field theory, we consider the class of extremal Kerr-Sen black hole (that contains three non-gravitational fields) as a class of solutions in the low energy limit (effective field theory) of heterotic string theory. We derive the expression of the conserved charges for the extremal Kerr-Sen solutions that contain dilaton, abelian gauge filed and antisymmetric tensor filed. We confirm and extend the validity of the conjecture (that the central charges from the non-gravitational fields vanish) for theories including antisymmetric tensor fields. We combine the calculated central charges with the expected form of the temperature using the Cardy formula to obtain the entropy of the extremal black hole microscopically; in agreement with the macroscopic Bekenstein-Hawking entropy of the extremal black hole.Comment: 14 pages, a few sentences added to the introduction, version to appear in JHE

Boundary Terms, Spinors and Kerr/CFT

Similarly as in AdS/CFT, the requirement that the action for spinors be stationary for solutions to the Dirac equation with fixed boundary conditions determines the form of the boundary term that needs to be added to the standard Dirac action in Kerr/CFT. We determine this boundary term and make use of it to calculate the two-point function for spinor fields in Kerr/CFT. This two-point function agrees with the correlator of a two dimensional relativistic conformal field theory.Comment: 15 page

SL(2,R)SL(2,R) symmetry and quasi-normal modes in the BTZ black hole

With the help of two new intrinsic tensor fields associated with the $SL(2,R)$ quadratic Casimir of Killing fields, we uncover the $SL(2,R)$ symmetry satisfied by the solutions to the equations of motion for various fields in the BTZ black hole in a uniform way by performing tensor and spinor analysis without resorting to any specific coordinate system. Then with the standard algebraic method developed recently, we determine the quasi-normal modes for various fields in the BTZ black hole. As a result, the quasi-normal modes are given by the infinite tower of descendants of the chiral highest weight mode, which is in good agreement with the previous analytic result obtained by exactly solving equations of motion instead.Comment: JHEP style, 1+13 pages, version to appear in JHE

Conformal weights in the Kerr/CFT correspondence

It has been conjectured that a near-extreme Kerr black hole is described by a 2d CFT. Previous work has shown that CFT operators dual to axisymmetric gravitational perturbations have integer conformal weights. In this paper, we study the analogous problem in 5d. We consider the most general near-extreme vacuum black hole with two rotational symmetries. This includes Myers-Perry black holes, black rings and Kaluza-Klein black holes. We find that operators dual to gravitational (or electromagnetic or massless scalar field) perturbations preserving both rotational symmetries have integer conformal weights, the same for all black holes considered.Comment: 19 page

Microscopic Realization of the Kerr/CFT Correspondence

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 AdS_3 x S^2. The holographic duals are typically known 2D CFTs with central charges c_L=c_R=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 J_L and electric graviphoton charge Q obeying Q^3 \leq J_L^2. It is shown that in the maximally charged limit Q^3 -> J_L^2, the near-horizon geometry coincides precisely with the right-moving temperature T_R=0 limit of the black string with magnetic charge P=J_L^{1/3}. The known dual of the latter is identified as the c_L=c_R=6J_L CFT predicted by the Kerr/CFT correspondence. Moreover, at linear order away from maximality, one finds a T_R \neq 0 quotient of the AdS_3 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 Q^3<J_L^2, 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 c_L=c_R=6J_L CFT predicted by Kerr/CFT.Comment: 18 pages, no figure