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.
Highlights
A better understanding of the role of multipartite entanglement in holographic systems is a longstanding question in the field
We show that the contribution of hyperthreads to calculations of holographic entanglement entropy are generically finite
In this article we have defined hyperthreads and shown that their maximal configurations are equivalent to various classes of minimal surfaces in the bulk
Summary
We will first review bipartite 2-threads in holographic spacetimes. Given a holographic spacetime M we take a constant time slice Σ and partition the boundary ∂Σ into two regions A and B. We will apply strong duality to the convex optimization program (2.6) This is done in two steps: first, we construct a Lagrangian from the objective using Lagrange multipliers to impose the constraints. The dualization of the minimization program must be modified so that we require each thread to cross a total barrier of at least 2. This is such that the threads of an optimal configuration saturate both mA and mB (which in this case because of purity are the same). In order for the constraints to be satisfied the minimal barrier configuration must include a surface which separates each boundary region from the others. This result, which is simple to prove in the context of measure theory, is considerably more difficult to show using flows [7]
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