Entanglement Wedges for Gravitating Regions

Motivated by properties of tensor networks, we conjecture that an arbitrary gravitating region $a$ can be assigned a generalized entanglement wedge $E\supset a$, such that quasi-local operators in $E$ have a holographic representation in the full algebra generated by quasi-local operators in $a$. The universe need not be asymptotically flat or AdS, and $a$ need not be asymptotic or weakly gravitating. On a static Cauchy surface $\Sigma$, 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, 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.Comment: 26 pages, 11 figure