Curved Corner Contribution to the Entanglement Entropy in an Anisotropic Spacetime

Abstract

We study the holographic entanglement entropy of anisotropic and nonconformal theories that are holographically dual to geometries with hyperscaling violation, parameterized by two parameters $z$ and $\theta$. In the vacuum state of a conformal field theory, it is known that the entanglement entropy of a kink region contains a logarithmic universal term which is only due to the singularity of the entangling surface. But, we show that the effects of the singularity as well as anisotropy of spacetime on the entanglement entropy exhibit themselves in various forms depending on $z$ and $\theta$ ranges. We identify the structure of various divergences that may be appear in the entanglement entropy, specially those which give rise to a universal contribution in the form of the logarithmic or double logarithmic terms. In the range $z>1$, for values $z=2k/(2k-1)$ with some integer $k$ and $\theta=0$, Lifshitz geometry, we find a double logarithmic term. In the range $0<z$, for values $\theta=1-2n|z-1|$ with some integer $n$ we find a logarithmic term.Comment: 19 pages, 2 figs; v2: introduction and conclusion expanded, refs adde