Universal terms for the entanglement entropy in 2+1 dimensions

In this article, we explore the divergences and universal terms of the holographic entanglement entropy for singular regions in anisotropic and nonconformal theories that are holographically dual to geometries with a hyperscaling violation, parameterized by two parameters $z$ and $\theta$. We study a curved corner in anisotropic space with arbitrary $\theta$ and $z$. We choose the region to be shape invariant under the scaling of spacetime. For this case, we show that the con...

We compute universal finite corrections to entanglement entropy for generalised quantum Lifshitz models in arbitrary odd spacetime dimensions. These are generalised free field theories with Lifshitz scaling symmetry, where the dynamical critical exponent $z$ equals the number of spatial dimensions $d$, and which generalise the 2+1-dimensional quantum Lifshitz model to higher dimensions. We analyse two cases: one where the spatial manifold is a $d$-dimensional sphere and the e...

In a $d$-dimensional conformal field theory, it has been known that a relevant deformation operator with the conformal dimension, $\Delta=\frac{d+2}{2}$, generates a logarithmic correction to the entanglement entropy. In the large 't Hooft coupling limit, we can investigate such a logarithmic correction holographically by deforming an AdS space with a massive scalar field dual to the operator with $\Delta=\frac{d+2}{2}$. There are two sources generating the logarithmic correc...

We compute free energies as well as conformal anomalies associated with boundaries for a conformal free scalar field. To that matter, we introduce the family of spaces of the form $\mathbb{S}^a\times \mathbb{H}^b$, which are conformally related to $\mathbb{S}^{a+b}$. For the case of $a=1$, related to the entanglement entropy across $\mathbb{S}^{b-1}$, we provide some new explicit computations of entanglement entropies at weak coupling. We then compute the free energy for spac...

In previous work universal behavior was conjectured for the behavior of the logarithmic terms in the entanglement entropy of intervals in 1+1 dimensional interface conformal field theories (ICFTs). These putative universal terms were exhibited both in free field theories as well as a large class of holographic models. In this work we demonstrate that this same behavior in fact is realized in any holographic ICFT, significantly strengthening the case for the conjecture.

The entanglement entropy correlates two quantum sub-systems which are the part of the larger system. A logarithmic divergence term present in the entanglement entropy is universal in nature and directly proportional to the conformal anomaly. We study this logarithmic divergence term of entropy for massive scalar field in $(2+1)$ dimension by applying numerical techniques to entanglement entropy approach. This (2+1) dimensional massive theory can be obtained from (3+1) dim...

We study the universal logarithmic coefficient of the entanglement entropy (EE) in a sphere for free fermionic field theories in a $d=4$ Minkowski spacetime. As a warm-up, we revisit the free massless spin-$1/2$ field case by employing a dimensional reduction to the $d=2$ half-line and a subsequent numerical real-time computation on a lattice. Surprisingly, the area coefficient diverges for a radial discretization but is finite for a geometric regularization induced by the mu...

We propose a simple approach to the calculation of the entanglement entropy of a spherically symmetric quantum system composed of two separate regions. We consider bound states of the system described by a wave function that is scale invariant and vanishes exponentially at infinity. Our result is in accordance with the holographic bound on entropy and shows that entanglement entropy scales with the area of the boundary.

We calculate the entanglement entropy for a sphere and a massless scalar field in any dimensions. The reduced density matrix is expressed in terms of the infinitesimal generator of conformal transformations keeping the sphere fixed. The problem is mapped to the one of a thermal gas in a hyperbolic space and solved by the heat kernel approach. The coefficient of the logarithmic term in the entropy for 2 and 4 spacetime dimensions are in accordance with previous numerical and a...

It has long been conjectured that the entropy of quantum fields across boundaries scales as the boundary area. This conjecture has not been easy to test in spacetime dimensions greater than four because of divergences in the von Neumann entropy. Here we show that the Renyi entropy provides a convergent alternative, yielding a quantitative measure of entanglement between quantum field theoretic degrees of freedom inside and outside hypersurfaces. For the first time, we show th...