A Semiclassical Diagnostic for Spacetime Emergence

TL;DR

The paper introduces a semiclassical diagnostic tool based on evanescent quantum extremal surfaces to identify failures in spacetime emergence within holography, and explores how observer rules can address these issues.

Contribution

It proposes a new diagnostic involving evanescent QES to detect emergence failures and assesses the role of observer rules in restoring spacetime emergence.

Findings

Evanescent QES are characterized by an upper bound on their area.

Their generalized entropy can be large despite small area, due to bulk entanglement.

The diagnostic distinguishes classical and quantum connectivity in semiclassical gravity.

Abstract

Recent developments have shown that some semiclassical spacetimes cannot emerge from a traditional application of the rules of holography, prompting proposals for restoring their emergence with "observer rules". In this paper, we propose a general semiclassical diagnostic of such failures of emergence, and of the extent to which observer rules can fix them. Our diagnostic is the presence of certain "evanescent" quantum extremal surfaces, which are distinguished by an upper bound on their area rather than their generalized entropy. In particular, the generalized entropy of an evanescent QES may be large: even though its area term must be small, its bulk entanglement term is unconstrained. This feature is explained by an operational distinction between classical and quantum connectivity in semiclassical gravity, or equivalently between the two summands of the generalized entropy.