Holographic Phases of Renyi Entropies

Understand

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 $n$.