Causality and Entanglement in Holography: The Connected Wedge Theorem Revisited

One puzzling aspect of holography is that it conjectures a duality between a physical theory with a single rigid causal structure (the non-gravitational "boundary theory") and one whose causal structure is state-dependent (the gravitational "bulk theory"). In this talk, I will explain how consistency of holographic quantum gravity can be used to constrain the entanglement structure of a field theory state based on which sets of boundary points admit causal scattering in its gravitational dual. This constraint can be argued for directly in the boundary theory using information-theoretic reasoning, and shown to hold in the bulk theory as a consequence of the quantum extremal surface formula for holographic entanglement entropy. I will also discuss how the gravitational reasoning used in this work suggests theorems about relativistic information processing that can be proved directly in information theory, without any reference to quantum gravity. Based on 1912.05649 and 2210.00018.