On sufficient conditions for holographic scattering

Abstract

Holography implies scattering in the bulk can be mediated by entanglement on the boundary. The connected wedge theorem (CWT) of May, Penington, and Sorce is a concrete example where bulk scattering implies correlation between certain boundary regions. However the converse does not hold. We investigate a recent proposal of Leutheusser and Liu for a generalization of the CWT with converse. We prove the forward direction: having pairs of CFT ``input'' (and likewise ``output'') regions in a phase with connected entanglement wedge implies that a particular bulk subregion (the intersection of ``input'' and ``output'' entanglement wedges) is non-empty. We then establish a modified version of the proposal which has a converse, and identify counter-examples to the stronger conjecture.