Holographic entanglement negativity for disjoint subsystems in $\mathrm{AdS_{d+1}/CFT_d}$

TL;DR

This paper introduces a holographic method to compute entanglement negativity for disjoint subsystems in higher-dimensional conformal field theories, extending previous AdS3/CFT2 results to more complex geometries.

Contribution

It proposes a new construction for holographic entanglement negativity in higher dimensions based on bulk RT surface areas, generalizing the AdS3/CFT2 approach.

Findings

Derived a formula for negativity in higher-dimensional CFTs

Computed negativity for disjoint rectangular subsystems in AdS and black hole backgrounds

Validated the approach through perturbative calculations

Abstract

We propose a construction to compute the holographic entanglement negativity for bipartite mixed state configurations of two disjoint subsystems in higher dimensional conformal field theories (CFT$_d$s) dual to bulk AdS$_{d+1}$ geometries. Our proposal follows from the corresponding AdS$_3$/CFT$_2$ scenario and involves an algebraic sum of the areas of bulk RT surfaces for certain combinations of subsystems. Utilizing our construction we compute the holographic entanglement negativity at the leading order through a perturbative expansion, for such bipartite mixed states of two disjoint subsystems with long rectangular strip geometries in CFT$_d$s dual to bulk pure AdS$_{d+1}$ geometries and AdS$_{d+1}$-Schwarzschild black holes.