Curved Corner Contribution to the Entanglement Entropy in an Anisotropic Spacetime

TL;DR

This paper investigates how curved corners in anisotropic, nonconformal holographic theories influence entanglement entropy, revealing dependence on parameters $z$ and $ heta$, and identifying universal divergence structures including logarithmic terms.

Contribution

It provides a detailed analysis of the divergence structure of holographic entanglement entropy for singular regions in anisotropic, hyperscaling-violating geometries, highlighting the dependence on $z$ and $ heta$ parameters.

Findings

Double logarithmic divergence for Lifshitz geometry with specific $z$ and $ heta$.

Logarithmic divergence for certain $ heta$ and $z$ ranges.

Universal contributions depend on the anisotropic parameters.

Abstract

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 contribution of the singularity to the entanglement entropy depends on $z$ and $\theta$ values. We identify the structure of various divergences that may appear, especially those which give rise to a universal contribution in the form of 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 $z<0$, for values $\theta=1-2n|z-1|$ with some integer $n$ we find a logarithmic term.