The associahedron as a holographic entanglement polytope

TL;DR

This paper explores an analogy between the associahedron used in scattering amplitudes and a holographic entanglement polytope in AdS/CFT, suggesting a link between amplitude factorization and space-time separability.

Contribution

It proposes interpreting the associahedron as a holographic entanglement polytope within the AdS/CFT framework, connecting scattering amplitudes to space-time structure.

Findings

Identifies an analogy between ABHY associahedron and entanglement structures in AdS/CFT.

Suggests a connection between amplitude factorization and holographic space-time separability.

Proposes the associahedron as a geometric object encoding entanglement patterns.

Abstract

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.