On shape dependence of holographic mutual information in AdS4

TL;DR

This paper investigates how the shape of boundary regions in AdS4 influences holographic mutual information, using numerical methods to analyze various geometries and identify transition points where mutual information disappears.

Contribution

It introduces a numerical approach to study shape dependence of holographic mutual information in AdS4 and explores a variety of boundary geometries.

Findings

Mutual information depends on the shape of boundary regions.

Transition curves where mutual information vanishes are identified.

Numerical results agree with known analytic cases.

Abstract

We study the holographic mutual information in AdS4 of disjoint spatial domains in the boundary which are delimited by smooth closed curves. A numerical method which approximates a local minimum of the area functional through triangulated surfaces is employed. After some checks of the method against existing analytic results for the holographic entanglement entropy, we compute the holographic mutual information of equal domains delimited by ellipses, superellipses or the boundaries of two dimensional spherocylinders, finding also the corresponding transition curves along which the holographic mutual information vanishes.