New conditions for multipartite entanglement wedge connectivity in $n$-to-$n$ holographic scattering

Abstract

We investigate the geometry of entanglement wedges for asymptotic $n$-to-$n$ scattering configurations in asymptotically AdS$_3$ spacetimes. Extending the $2$-to-$2$ Connected Wedge Theorem, we establish a strictly weaker sufficient condition for the input entanglement wedge $\mathcal{E}(V_1\cup\cdots\cup V_n)$ to be connected: the existence of a single pair of input regions satisfying a $2$-to-all causal intersection condition already forces full multipartite wedge connectivity. We also derive novel necessary conditions, showing that when the input wedge is connected, certain output ridges must enter the input wedge, and we organize these consequences into a layered reduction on the boundary lattice. Furthermore, we analyze the generalized bulk scattering region $\mathcal{S}_E = \mathcal{E}(V_1\cup\cdots\cup V_n)\cap \mathcal{E}(W_1\cup\cdots\cup W_n)$ and obtain necessary conditions for it to be nonempty; for $n>2$ these conditions are stronger than mere wedge connectedness. Our results provide new geometric restrictions on multipartite entanglement in holography and clarify the holographic dictionary for multi-partite scattering processes, while also highlighting intrinsic limitations for $n>2$.