Beyond $2$-to-$2$: Geometrization of Entanglement Wedge Connectivity in Holographic Scattering

TL;DR

This paper generalizes the Connected Wedge Theorem to multi-particle holographic scattering, providing new conditions for entanglement wedge connectivity and refining the geometric-quantum entanglement correspondence.

Contribution

It extends the theorem to n-to-n scatterings, offering a weaker necessary condition and a new sufficient condition for boundary entanglement wedge connectivity.

Findings

Derived a weaker necessary condition for entanglement wedge connectedness.

Proved a novel sufficient condition for entanglement wedge connectivity.

Analyzed criteria for non-empty entanglement wedge intersection regions.

Abstract

We extend recent discussions on generalization of the Connected Wedge Theorem about $2$-to-$2$ holographic scattering problem to $n$-to-$n$ scatterings ($n>2$). In this broader setting, our theorem provides a weaker necessary condition for the connectedness of boundary entanglement wedges than previously identified. Besides, we prove a novel sufficient condition for this connectedness. We also present an analysis of the criteria ensuring a non-empty entanglement wedge intersection region $\mathcal{S}_E$. These results refine the holographic dictionary between geometric connectivity and quantum entanglement for general multi-particle scattering.