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Universality of corner entanglement in conformal field theories

Pablo Bueno, Robert C. Myers, William Witczak-Krempa

TL;DR

It is shown that the ratio a(θ)/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.

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 $a(θ)$ 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 $a(θ)/C_T$, 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 $θ\rightarrow π$, where the entangling surface approaches a smooth curve. We thus conjecture that the corresponding ratio is universal for general CFTs in three dimensions.

Universality of corner entanglement in conformal field theories

TL;DR

It is shown that the ratio a(θ)/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.

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 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 , where 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 models with . Strikingly, the agreement between these different theories becomes exact in the limit , where the entangling surface approaches a smooth curve. We thus conjecture that the corresponding ratio is universal for general CFTs in three dimensions.

Paper Structure

This paper contains 3 sections, 49 equations, 2 figures, 1 table.

Table of Contents

  1. Holographic calculations
  2. Field theory calculations of $\sigma$
  3. Corner coefficient $a(\theta)$ for the extensive mutual information model

Figures (2)

  • Figure 1: a) An entangling region $V$ of size $\ell$ with a corner; b) The holographic entangling surface $\gamma$ for a region on the boundary of AdS$_4$ with a corner.
  • Figure 2: (Top) $a(\theta)/C_{ T}$ from holography (gray), a free Dirac fermion (red) and a scalar (blue), plus the corresponding lattice data points obtained numerically Casini:2006hu (red/blue squares). We also show $a(\pi/2)/C_{ T}$ for the $N\!=\!1,2,3$ Wilson-Fisher $O(N)$ CFTs, and the trial function (\ref{['Swingle']}) (purple). (Bottom) Same quantities normalized by $[a(\theta)/C_{ T}]_{\rm holo}$.