Holographic Phases of Renyi Entropies

TL;DR

This paper explores phase transitions in Renyi entropies of conformal field theories via holography, showing how scalar operator dimensions influence black hole stability and entropy behavior.

Contribution

It reveals a connection between scalar operator dimensions and phase transitions in holographic Renyi entropies, extending understanding of entanglement in CFTs.

Findings

Phase transition in Renyi entropies at a critical parameter value

Black hole instability linked to scalar operator dimension

Spectrum of reduced density matrix depends on scalar operator spectrum

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 $\rho$, depends on the dimension of the lowest dimension non-trivial scalar operator in the theory.