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Black Hole Entropy Function, Attractors and Precision Counting of Microstates
, 2007
"... In these lecture notes we describe recent progress in our understanding of attractor mechanism and entropy of extremal black holes based on the entropy function formalism. We also describe precise computation of the microscopic degeneracy of a class of quarter BPS dyons in N = 4 supersymmetric strin ..."
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Cited by 324 (28 self)
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In these lecture notes we describe recent progress in our understanding of attractor mechanism and entropy of extremal black holes based on the entropy function formalism. We also describe precise computation of the microscopic degeneracy of a class of quarter BPS dyons in N = 4 supersymmetric string theories, and compare the statistical entropy of these dyons, expanded in inverse powers of electric and magnetic charges, with a similar expansion of the corresponding black hole entropy. This comparison is extended to include the contribution to the entropy from multicentered black holes as well.
Holographic Entanglement Entropy: An Overview
, 2009
"... In this article, we review recent progresses on the holographic understandings of the entanglement entropy in the AdS/CFT correspondence. After reviewing the general idea of holographic entanglement entropy, we will explain its applications to confinement/deconfinement phase transitions, black hole ..."
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Cited by 120 (12 self)
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In this article, we review recent progresses on the holographic understandings of the entanglement entropy in the AdS/CFT correspondence. After reviewing the general idea of holographic entanglement entropy, we will explain its applications to confinement/deconfinement phase transitions, black hole entropy and covariant formulation of holography.
Near Extremal Black Hole Entropy as Entanglement Entropy via AdS2/CFT1
, 2007
"... We point out that the entropy of (near) extremal black holes can be interpreted as the entanglement entropy of dual conformal quantum mechanics via AdS2/CFT1. As an explicit example, we study near extremal BTZ black holes and derive this claim from AdS3/CFT2. We also analytically compute the entangl ..."
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Cited by 48 (8 self)
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We point out that the entropy of (near) extremal black holes can be interpreted as the entanglement entropy of dual conformal quantum mechanics via AdS2/CFT1. As an explicit example, we study near extremal BTZ black holes and derive this claim from AdS3/CFT2. We also analytically compute the entanglement entropy in the two dimensional CFT of a free Dirac fermion compactified on a circle at finite temperature. From this result, we clarify the relation between the thermal entropy and entanglement entropy, which is essential for the entanglement interpretation of black hole entropy.
Extremal Black Hole and Flux Vacua Attractors
, 2007
"... These lectures provide a pedagogical, introductory review of the socalled Attractor Mechanism (AM) at work in two different 4dimensional frameworks: extremal black holes in N = 2 supergravity and N = 1 flux compactifications. In the first case, AM determines the stabilization of scalars at the bla ..."
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Cited by 23 (15 self)
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These lectures provide a pedagogical, introductory review of the socalled Attractor Mechanism (AM) at work in two different 4dimensional frameworks: extremal black holes in N = 2 supergravity and N = 1 flux compactifications. In the first case, AM determines the stabilization of scalars at the black hole event horizon purely in terms of the electric and magnetic charges, whereas in the second context the AM is responsible for the stabilization of the universal axiondilaton and of the (complex structure) moduli purely in terms of the RR and NSNS fluxes. Two equivalent approaches to AM, namely the socalled “criticality conditions ” and “New Attractor ” ones, are analyzed in detail in both frameworks, whose analogies and differences are discussed. Also a stringy analysis of both frameworks (relying on Hodgedecomposition techniques) is performed, respectively considering 2 CY3×T Type IIB compactified on CY3 and its orientifolded version, associated with. Finally, recent Z2 results on the Uduality orbits and moduli spaces of nonBPS extremal black hole attractors in
Near the horizon of 5D black rings
, 810
"... Abstract: For the five dimensional N = 2 black rings, we study the supersymmetry enhancement and identify the global supergroup of the near horizon geometry. We show that the global part of the supergroup is OSp(4 ∗ 2) × SL(2) which is the same as the small black string. We show that results obtai ..."
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Cited by 7 (2 self)
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Abstract: For the five dimensional N = 2 black rings, we study the supersymmetry enhancement and identify the global supergroup of the near horizon geometry. We show that the global part of the supergroup is OSp(4 ∗ 2) × SL(2) which is the same as the small black string. We show that results obtained by applying the entropy function formalism and the cextremization approach to the black ring solution are in agreement with the microscopic entropy calculation. Also, we extend our calculation to the small black ring solution and compute the modification of the corresponding parameters.
Central Charges in Extreme Black Hole/CFT Correspondence, arXiv:0902.1001 [hepth
 CFT Duals for Attractor Horizons, arXiv:0902.4033 [hepth
"... Abstract: The Kerr/CFT correspondence has been recently broadened to the general extremal black holes under the assumption that the central charges from the nongravitational fields vanish. To confirm this proposal, we derive the expression of the conserved charges in the EinsteinMaxwellscalar the ..."
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Abstract: The Kerr/CFT correspondence has been recently broadened to the general extremal black holes under the assumption that the central charges from the nongravitational fields vanish. To confirm this proposal, we derive the expression of the conserved charges in the EinsteinMaxwellscalar theory with topological terms in four and five dimensions and check that the above assumption was correct. Combining the computed central charge with the expected form of the temperature, the BekensteinHawking entropy of the general extremal black holes in four and five dimensions can be reproduced by using the Cardy formula. Keywords: Black holes, Conservation laws, Conformal field theory, AdS/CFT. Contents
The Kerr/CFT Correspondence and String Theory
"... The Kerr/CFT correspondence is a holographic duality between a two dimensional chiral CFT and the very near horizon limit of an extremal black hole, which includes the AdS2 structure. To understand the dual chiral CFT2, we apply the Kerr/CFT correspondence to a certain class of black holes embedded ..."
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Cited by 3 (0 self)
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The Kerr/CFT correspondence is a holographic duality between a two dimensional chiral CFT and the very near horizon limit of an extremal black hole, which includes the AdS2 structure. To understand the dual chiral CFT2, we apply the Kerr/CFT correspondence to a certain class of black holes embedded in string theory, which includes the D1D5P and the BMPV black hole, and obtain the correct entropies for the black holes microscopically. These have the AdS3 throat in the near horizon geometry and the AdS2 throat in the very near horizon geometry. We identified one of the two Virasoros in the nonchiral CFT2 dual to the AdS3, i.e. in the AdS3/CFT2, with the Virasoro in the chiral CFT2 dual to the AdS2, i.e. in the Kerr/CFT correspondence. We also discuss a way to understand the chiral CFT2 dual to generic extremal black holes. A kind of universality for the very near horizon geometries of extremal black holes will be important for the validity of the Kerr/CFT correspondence. Based on this analysis, we propose that the Kerr/CFT correspondence can be understood as a decoupling limit in which only the ground states remain.
CERNPHTH/2008020 d = 4 Black Hole Attractors in N = 2 Supergravity with FayetIliopoulos Terms
, 802
"... We generalize the description of the d = 4 Attractor Mechanism based on an effective black hole (BH) potential to the presence of a gauging which does not modify the derivatives of the scalars and does not involve hypermultiplets. The obtained results do not rely necessarily on supersymmetry, and th ..."
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Cited by 3 (0 self)
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We generalize the description of the d = 4 Attractor Mechanism based on an effective black hole (BH) potential to the presence of a gauging which does not modify the derivatives of the scalars and does not involve hypermultiplets. The obtained results do not rely necessarily on supersymmetry, and they can be extended to d> 4, as well. Thence, we work out the example of the stu model of N = 2 supergravity in the presence of FayetIliopoulos terms, for the supergravity analogues of the magnetic and D0 − D6 BH charge configurations, and in three different symplectic frames: the (SO (1, 1)) 2, SO (2, 2) covariant and SO (8)truncated ones. The attractive nature of the critical points, related to the semipositive definiteness of the Hessian