Universality of corner entanglement in conformal field theories

TL;DR

This paper investigates the corner contribution to entanglement entropy in 3D conformal field theories, revealing an almost universal ratio of this contribution to the central charge across diverse models, especially near smooth entangling surfaces.

Contribution

It demonstrates the near universality of the ratio between corner entanglement and the stress tensor central charge in various 3D CFTs, including holographic and free theories, especially as the corner angle approaches π.

Findings

The ratio a(θ)/C_T is nearly universal across different theories.

Universality becomes exact as the corner angle approaches π.

Supports the conjecture of a universal corner entanglement measure in 3D CFTs.

Abstract

We study the contribution to the entanglement entropy of (2+1)-dimensional conformal field theories coming from a sharp corner in the entangling surface. This contribution is encoded in a function $a(\theta)$ of the corner opening angle, and was recently proposed as a measure of the degrees of freedom in the underlying CFT. We show that the ratio $a(\theta)/C_T$, where $C_T$ is the central charge in the stress tensor correlator, is an almost universal quantity for a broad class of theories including various higher-curvature holographic models, free scalars and fermions, and Wilson-Fisher fixed points of the $O(N)$ models with $N=1,2,3$. Strikingly, the agreement between these different theories becomes exact in the limit $\theta\rightarrow \pi$, where the entangling surface approaches a smooth curve. We thus conjecture that the corresponding ratio is universal for general CFTs in three dimensions.