Universality of corner entanglement in conformal field theories

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.