Locality from Quantum Gravity: All or Nothing

In a full theory of quantum gravity, local physics is expected to be approximate rather than innate. It is therefore important to understand how approximate locality emerges in the semiclassical limit. Here we show that any notion of locality emergent from a holographic theory of quantum gravity is "all or nothing": local data is not obtained gradually from subregions of the boundary, but is rather obtained all at once when enough of the boundary is accessed. Our assumptions are mild and thus this feature is quite general; in the special case of AdS/CFT, a slightly different manifestation follows from well-known and familiar properties.Comment: 7 pages; 4 figures. v2: added references, minor edit

Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime

We propose that holographic entanglement entropy can be calculated at arbitrary orders in the bulk Planck constant using the concept of a "quantum extremal surface": a surface which extremizes the generalized entropy, i.e. the sum of area and bulk entanglement entropy. At leading order in bulk quantum corrections, our proposal agrees with the formula of Faulkner, Lewkowycz, and Maldacena, which was derived only at this order; beyond leading order corrections, the two conjectures diverge. Quantum extremal surfaces lie outside the causal domain of influence of the boundary region as well as its complement, and in some spacetimes there are barriers preventing them from entering certain regions. We comment on the implications for bulk reconstruction.Comment: 28 pages, 6 figures. Version 3: typos fixed, minor changes to reference