We study the contribution to the entanglement entropy of ($2+1$)-dimensional conformal field theories (CFTs) 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 $\theta \to \pi$, where the entangling surface approaches a smooth curve. We thus conjecture that the corresponding ratio is universal for general CFTs in three dimensions.

• Received 1 June 2015

DOI:https://doi.org/10.1103/PhysRevLett.115.021602