A holographic proof of the universality of corner entanglement for CFTs

TL;DR

This paper provides a holographic proof for the universal ratio of corner entanglement coefficients in 3d CFTs and explores related universal behaviors in higher dimensions using higher curvature gravity models.

Contribution

It offers a holographic proof of the conjectured universality of the ratio / for 3d CFTs and investigates the universality and bounds of corner entanglement coefficients in higher dimensions.

Findings

Confirmed the universality of / ratio in 3d CFTs.

Found that /C_T is universal, but /C_T is not.

Identified universal laws for corner entanglement in higher dimensions.

Abstract

There appears a universal logarithmic term of entanglement entropy, i.e., $-a(\Omega) \log(H/\delta)$, for 3d CFTs when the entangling surface has a sharp corner. $a(\Omega)$ is a function of the corner opening angle and behaves as $a(\Omega\to \pi)\simeq \sigma (\pi-\Omega)^2$ and $a(\Omega\to 0)\simeq \kappa/\Omega$, respectively. Recently, it is conjectured that $\sigma/C_T=\pi^2/24 $, where $C_T$ is central charge in the stress tensor correlator, is universal for general CFTs in three dimensions. In this paper, by applying the general higher curvature gravity, we give a holographic proof of this conjecture. We also clarify some interesting problems. Firstly, we find that, in contrast to $\sigma/C_T$, $\kappa/C_T$ is not universal. Secondly, the lower bound $a_E(\Omega)/C_T$ associated to Einstein gravity can be violated by higher curvature gravity. Last but not least, we find that there are similar universal laws for CFTs in higher dimensions. We give some holographic tests of these new conjectures.