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48
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.
Entanglement entropy and conformal field theory
, 2009
"... We review the conformal field theory approach to entanglement entropy. We show how to apply these methods to the calculation of the entanglement entropy of a single interval, and the generalization to different situations such as finite size, systems with boundaries, and the case of several disjoint ..."
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Cited by 92 (11 self)
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We review the conformal field theory approach to entanglement entropy. We show how to apply these methods to the calculation of the entanglement entropy of a single interval, and the generalization to different situations such as finite size, systems with boundaries, and the case of several disjoint intervals. We discuss the behaviour away from the critical point and the spectrum of the reduced density matrix. Quantum quenches, as paradigms of nonequilibrium situations, are also considered.
Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
, 2008
"... We review and extend recent attempts to find a precise relation between extremal black hole entropy and degeneracy of microstates using AdS2/CFT1 correspondence. Our analysis leads to a specific relation between degeneracy of black hole microstates and an appropriately defined partition function of ..."
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Cited by 34 (9 self)
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We review and extend recent attempts to find a precise relation between extremal black hole entropy and degeneracy of microstates using AdS2/CFT1 correspondence. Our analysis leads to a specific relation between degeneracy of black hole microstates and an appropriately defined partition function of string theory on the near horizon geometry, – named the quantum entropy function. In the classical limit this reduces to the usual relation between statistical
Holographic entanglement entropy: near horizon geometry and disconnected regions
 JHEP 1105 (2011) 004, arXiv:1011.0166 [hepth]. – 10
"... We study the finite term of the holographic entanglement entropy for the charged black hole in AdSd+2 and other examples of black holes when the spatial region in the boundary theory is given by one or two parallel strips. For one large strip it scales like the width of the strip. The divergent term ..."
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Cited by 13 (3 self)
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We study the finite term of the holographic entanglement entropy for the charged black hole in AdSd+2 and other examples of black holes when the spatial region in the boundary theory is given by one or two parallel strips. For one large strip it scales like the width of the strip. The divergent term of its expansion as the turning point of the minimal surface approaches the horizon is determined by the near horizon geometry. Examples involving a Lifshitz scaling are also considered. For two equal strips in the boundary we study the transition of the mutual information given by the holographic prescription. In the case of the charged black hole, when the width of the strips becomes large this transition provides a characteristic finite distance depending on the temperature. ar
Entanglement Entropy in Quantum Gravity and the Plateau Problem
, 711
"... In a quantum gravity theory the entropy of entanglement S between the fundamental degrees of freedom spatially divided by a surface is discussed. The classical gravity is considered as an emergent phenomenon and arguments are presented that: 1) S is a macroscopical quantity which can be determined w ..."
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Cited by 8 (2 self)
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In a quantum gravity theory the entropy of entanglement S between the fundamental degrees of freedom spatially divided by a surface is discussed. The classical gravity is considered as an emergent phenomenon and arguments are presented that: 1) S is a macroscopical quantity which can be determined without knowing a real microscopical content of the fundamental theory; 2) S is given by the BekensteinHawking formula in terms of the area of a codimension 2 hypesurface B; 3) in static spacetimes B can be defined as a minimal hypersurface of a least volume separating the system in a constant time slice. It is shown that properties of S are in agreement with basic properties of the von Neumann entropy. Explicit variational formulae for S in different physical examples are considered. 1 1
Entanglement Entropy and Higher Spin Holography
 in AdS3, JHEP 1404
, 2014
"... A holographic correspondence has been recently developed between higher spin theories in threedimensional antide Sitter space (AdS3) and twodimensional Conformal Field Theories (CFTs) with extended symmetries. A class of such dualities involves SL(N,R) × SL(N,R) ChernSimons gauge theories in th ..."
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Cited by 7 (2 self)
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A holographic correspondence has been recently developed between higher spin theories in threedimensional antide Sitter space (AdS3) and twodimensional Conformal Field Theories (CFTs) with extended symmetries. A class of such dualities involves SL(N,R) × SL(N,R) ChernSimons gauge theories in the (2+1)dimensional bulk spacetime, and CFTs with WN symmetry algebras on the (1+1)dimensional boundary. The topological character of the ChernSimons theory forces one to reconsider standard geometric notions such as black hole horizons and entropy, as well as the usual holographic dictionary. Motivated by this challenge, in this note we present a proposal to compute entanglement entropy in the WN CFTs via holographic methods. In particular, we introduce a functional constructed from Wilson lines in the bulk ChernSimons theory that captures the entanglement entropy in the CFTs dual to standard AdS3 gravity, corresponding to SL(2,R) × SL(2,R) gauge group, and admits an immediate generalization to the higher spin case. We explicitly evaluate this functional for several known solutions of the ChernSimons theory, including charged black holes dual to thermal CFT states carrying higher spin charge, and show that it reproduces expected features of entanglement entropy, study whether it obeys strong subadditivity, and moreover show that it reduces to the thermal entropy in the appropriate limit. ar X iv
Near Extremal Kerr Entropy from AdS2 Quantum Gravity,” arXiv:0908.1121 [hepth]. See also
"... We analyze the asymptotic symmetries of near extremal Kerr black holes in four dimensions using the AdS2/CFT1 correspondence. We find a Virasoro algebra with central charge cR = 12J that is independent from the Virasoro algebra (with the same central charge) that acts on the degenerate ground state. ..."
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Cited by 6 (0 self)
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We analyze the asymptotic symmetries of near extremal Kerr black holes in four dimensions using the AdS2/CFT1 correspondence. We find a Virasoro algebra with central charge cR = 12J that is independent from the Virasoro algebra (with the same central charge) that acts on the degenerate ground state. The energy of the excitations is computed as well, and we can use Cardy’s formula to determine the near extremal entropy. Our result is consistent with the BekensteinHawking area law for near extremal Kerr black holes. 1
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.