Entanglement wedges for gravitating regions

Abstract

Motivated by properties of tensor networks, we conjecture that an arbitrary gravitating region a can be assigned a generalized entanglement wedge Ea, such that quasilocal operators in E have a holographic representation in the full algebra generated by quasilocal operators in a. The Universe need not be asymptotically flat or anti-de Sitter (AdS), and a need not be asymptotic or weakly gravitating. On a static Cauchy surface ς, we propose that E is the superset of a that minimizes the generalized entropy. We prove that E satisfies a no-cloning theorem and appropriate forms of strong subadditivity and nesting. If a lies near a portion A of the conformal boundary of AdS space, our proposal reduces to the quantum minimal surface prescription applied to A. We also discuss possible covariant extensions of this proposal, although none prove completely satisfactory. Our results are consistent with the conjecture that information in E that is spacelike to a in the semiclassical description can nevertheless be recovered from a, by microscopic operators that break that description. We thus propose that E quantifies the range of holographic encoding, an important nonlocal feature of quantum gravity, in general spacetimes.