The associahedron as a holographic entanglement polytope

By employing the ${\rm AdS}_3/{\rm CFT}_2$ correspondence in this note we observe an analogy between the structures found in connection with the Arkani-Hamed-Bai-He-Yan (ABHY) associahedron used for understanding scattering amplitudes, and the one used for understanding space-time emerging from patterns of entanglement. The analogy suggests the natural interpretation for the associahedron as a holographic entanglement polytope associated to the ${\rm CFT}_2$ vacuum. Our observations hint at the possibility that the factorization properties of scattering amplitudes are connected to the notion of separability of space-time as used in the theory of holographic quantum entanglement.

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