Corner contributions to holographic entanglement entropy

TL;DR

This paper investigates how corner contributions to holographic entanglement entropy in 3D conformal field theories are affected by higher curvature gravity interactions, revealing universal ratios and agreement with free CFTs.

Contribution

It demonstrates that higher curvature terms only scale the corner contribution without changing its angular dependence, and proposes a universal ratio involving the corner term and stress tensor central charge.

Findings

Corner contribution is scaled by a universal factor in holographic models.

The ratio of corner contribution to stress tensor central charge is universal across models.

Good agreement with free CFT results, especially as the entangling surface becomes smooth.

Abstract

The entanglement entropy of three-dimensional conformal field theories contains a universal contribution coming from corners in the entangling surface. We study these contributions in a holographic framework and, in particular, we consider the effects of higher curvature interactions in the bulk gravity theory. We find that for all of our holographic models, the corner contribution is only modified by an overall factor but the functional dependence on the opening angle is not modified by the new gravitational interactions. We also compare the dependence of the corner term on the new gravitational couplings to that for a number of other physical quantities, and we show that the ratio of the corner contribution over the central charge appearing in the two-point function of the stress tensor is a universal function for all of the holographic theories studied here. Comparing this holographic result to the analogous functions for free CFT's, we find fairly good agreement across the full range of the opening angle. However, there is a precise match in the limit where the entangling surface becomes smooth, i.e., the angle approaches $\pi$, and we conjecture the corresponding ratio is a universal constant for all three-dimensional conformal field theories. In this paper, we expand on the holographic calculations in our previous letter arXiv:1505.04804, where this conjecture was first introduced.