A proof of the generalized Connected Wedge Theorem

A bstract In the context of asymptotic 2-to-2 scattering process in AdS/CFT, the Connected Wedge Theorem identifies the existence of O (1 /G N ) mutual information between suitable boundary subregions, referred to as decision regions, as a necessary but not sufficient condition for bulk-only scattering processes, i.e., nonempty bulk scattering region $${\mathcal{S}}_{0}$$ . Recently, Liu and Leutheusser proposed an enlarged bulk scattering region $${\mathcal{S}}_{E}$$ and conjectured that the non-emptiness of $${\mathcal{S}}_{E}$$ fully characterizes the existence of O (1 /G N ) mutual information between decision regions. Here, we provide a geometrical or general relativity proof for a slightly modified version of their conjecture.