# On shape dependence of holographic entanglement entropy in AdS4/CFT3 with Lifshitz scaling and hyperscaling violation

## TL;DR

This paper analyzes how the shape of regions affects the holographic entanglement entropy in Lifshitz spacetimes with hyperscaling violation, providing analytic formulas and numerical validation for various shapes.

## Contribution

It derives analytic expressions for divergent and finite terms of holographic entanglement entropy for arbitrary smooth shapes in Lifshitz backgrounds with hyperscaling violation.

## Key findings

- Analytic formulas for divergent and finite entanglement entropy terms.
- Numerical validation for disk and ellipse shapes.
- Results applicable to static and dynamic backgrounds.

## Abstract

We study the divergent terms and the finite term in the expansion of the holographic entanglement entropy as the ultraviolet cutoff vanishes for smooth spatial regions having arbitrary shape, when the gravitational background is a four dimensional asymptotically Lifshitz spacetime with hyperscaling violation, in a certain range of the hyperscaling parameter. Both static and time dependent backgrounds are considered. For the coefficients of the divergent terms and for the finite term, analytic expressions valid for any smooth entangling curve are obtained. The analytic results for the finite terms are checked through a numerical analysis focussed on disks and ellipses.