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Holographic phases of Rényi entropies

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Abstract

We consider Rényi entropies \( {S_n}=\frac{1}{1-n } \log\;\mathrm{Tr}{\rho^n} \) of conformal field theories in flat space, with the entangling surface being a sphere. The AdS/CFT correspondence relates this Rényi entropy to that of a black hole with hyperbolic horizon; as the Rényi parameter n increases the temperature of the black hole decreases. If the CFT possesses a sufficiently low dimension scalar operator the black hole will be unstable to the development of hair. Thus, as n is varied, the Rényi entropies will exhibit a phase transition at a critical value of n. The location of the phase transition, along with the spectrum of the reduced density matrix ρ, depends on the dimension of the lowest dimension non-trivial scalar operator in the theory.

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Authors and Affiliations

  1. Physics Department, McGill University, 3600 rue University, Montréal, QC, H3A 2T8, Canada

    Alexandre Belin, Alexander Maloney & Shunji Matsuura

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  1. Alexandre Belin
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  2. Alexander Maloney
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  3. Shunji Matsuura
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Correspondence to Shunji Matsuura.

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ArXiv ePrint: 1306.2640

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Belin, A., Maloney, A. & Matsuura, S. Holographic phases of Rényi entropies. J. High Energ. Phys. 2013, 50 (2013). https://doi.org/10.1007/JHEP12(2013)050

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  • DOI: https://doi.org/10.1007/JHEP12(2013)050

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