Corner contributions to holographic entanglement entropy

TL;DR

The paper analyzes universal corner contributions to the entanglement entropy of 3D CFTs in holographic models with higher-curvature bulk gravity. It finds that, across curvature-squared and generalized Lovelock theories, the entire function a(Ω) is preserved up to an overall coupling-dependent factor, and the ratio κ/C_T remains universal at linear order. By comparing to free CFTs and disk/strip entropies, it shows that while some charges align across theories, others depend on bulk couplings, offering a calibrated benchmark for comparing three-dimensional CFTs. The work further conjectures a universal constant σ/C_T for the smooth limit and highlights that a normalized corner function a(Ω)/C_T provides a robust cross-theory diagnostic. Overall, the results support a universal normalization framework while leaving open whether the full angular dependence can be modified in more general higher-curvature theories.

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 $π$, 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.

Figures (6)

• Figure 1: (Colour online) A corner in the entangling surface with opening angle $\Omega$.
• Figure 2: (Colour online) A kink in a constant Euclidean time slice $t_E=0$ in the boundary of AdS$_4$.
• Figure 3: (Colour online) (a) $\Omega/\pi$ as a function of $h_0$ and (b) ${ \frac{2G}{\tilde{L}^2}}\,a$ as a function of $\Omega/\pi$. In the second panel, the dashed lines correspond to the approximate expressions derived in eqs. (\ref{['lim1']}) and (\ref{['lim2']}) for small opening angles (red) and the smooth limit (orange), respectively.
• Figure 4: (Colour online) We show $a(\Omega)/\kappa$ for AdS/CFT (orange), a free scalar (blue), a free fermion (red) and the lattice points (squares) obtained numerically for three values of $\Omega$Casini:2006hu. We also include the black dashed curve giving the $1/\Omega$ behavior which all of the functions will approach for small angles.
• Figure 5: (Colour online) We show $(a(\Omega)/\kappa)_{\rm free}/(a(\Omega)/\kappa)_{\rm holo}$ both for the free scalar (blue), the free fermion (red) and the corresponding lattice results (squares). We also show the interpolated curves obtained using the 14 coefficients of the Taylor expansions around $\Omega=\pi$ as well as the coefficients $\kappa$ in the small opening angle expansions (dashed blue and red). The black dashed line would correspond to the value for which the ratios are equal. Both theories will in fact approach the black square at the end of this line, i.e., at $\Omega=0$, a behaviour that is captured by the interpolated functions.