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      Large N Phase Transitions, Finite Volume, and Entanglement Entropy

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          Abstract

          Holographic studies of the entanglement entropy of field theories dual to charged and neutral black holes in asymptotically global AdS4 spacetimes are presented. The goal is to elucidate various properties of the quantity that are peculiar to working in finite volume, and to gain access to the behaviour of the entanglement entropy in the rich thermodynamic phase structure that is present at finite volume and large N. The entropy is followed through various first order phase transitions, and also a novel second order phase transition. Properties of a specific heat in the neighbourhood of the critical point are computed. Behaviour is found that contrasts interestingly with an earlier holographic study of a second order phase transition dual to an holographic superconductor.

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          Generalized second law of thermodynamics in black-hole physics

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            Holographic Derivation of Entanglement Entropy from AdS/CFT

             ,   (2010)
            A holographic derivation of the entanglement entropy in quantum (conformal) field theories is proposed from AdS/CFT correspondence. We argue that the entanglement entropy in d+1 dimensional conformal field theories can be obtained from the area of d dimensional minimal surfaces in AdS_{d+2}, analogous to the Bekenstein-Hawking formula for black hole entropy. We show that our proposal perfectly reproduces the correct entanglement entropy in 2D CFT when applied to AdS_3. We also compare the entropy computed in AdS_5 \times S^5 with that of the free N=4 super Yang-Mills.
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              Black holes and thermodynamics

               S. Hawking (1976)
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                Author and article information

                Journal
                20 June 2013
                2013-08-23
                Article
                10.1007/JHEP03(2014)047
                1306.4955

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                JHEP 1403 (2014) 047
                19 pages, 9 multi-component figures (v3: Section 4.1 reduced in scope due to ansatz error in earlier versions. v4: Expanded version with several more results including study of specific heat and critical exponents.)
                hep-th

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