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

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.