Hyperthreads in holographic spacetimes

TL;DR

This paper introduces hyperthreads, a generalization of bit threads connecting multiple boundary regions, to better understand multipartite entanglement in holographic spacetimes, providing finite contributions and new measures.

Contribution

It defines hyperthreads as units of multipartite entanglement and links their maximal contributions to surface areas, advancing holographic entanglement entropy calculations.

Findings

Hyperthreads connect multiple boundary regions.

Hyperthread contributions to entropy are finite.

Surface areas relate to maximum hyperthread counts.

Abstract

We generalize bit threads to hyperthreads in the context of holographic spacetimes. We define a "$k$-thread" to be a hyperthread which connects $k$ different boundary regions and posit that it may be considered as a unit of $k$-party entanglement. Using this new object, we show that the contribution of hyperthreads to calculations of holographic entanglement entropy are generically finite. This is accomplished by constructing a surface whose area determines their maximum allowed contribution. We also identify surfaces whose area is proportional to the maximum number of $k$-threads, motivating a possible measure of multipartite entanglement. We use this to make connections to the current understanding of multipartite entanglement in holographic spacetimes.