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arXiv · 1306.2640

Holographic Phases of Renyi Entropies

Alexandre Belin·Alexander Maloney·Shunji Matsuura
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Abstract

We consider Renyi entropies of conformal field theories in flat space, with the entangling surface being a sphere. The AdS/CFT correspondence relates this Renyi entropy to that of a black hole with hyperbolic horizon; as the Renyi 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 Renyi 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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Alexandre Belin, Alexander Maloney, Shunji Matsuura. 2015-01-20. Holographic Phases of Renyi Entropies. https://doi.org/10.1007/jhep12(2013)050

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