The Fate of Information Localizability and Holography in Quantum Gravity

TL;DR

This paper investigates the conditions under which information in quantum gravity can be localized or remains non-local, analyzing the implications for holography and bulk-boundary correspondence in AdS/CFT.

Contribution

It provides explicit examples where non-local information encoding can be observed or suppressed, highlighting limitations of perturbative holography in quantum gravity.

Findings

Non-local information encoding can be detected in semiclassical gravity.

Protocols for bulk excitation detection can be more efficient than boundary signals.

Holography may not hold perturbatively when information localization is suppressed.

Abstract

The AdS/CFT correspondence states an equivalence between a quantum gravitational theory in a (d+1)-dimensional anti-de Sitter spacetime (AdS$_{d+1}$) and a d-dimensional conformal field theory (CFT$_{d}$). The CFT$_{d}$ lives on the asymptotic boundary of the bulk AdS$_{d+1}$. Hence a local operator in the bulk of the AdS$_{d+1}$ should be reconstructable using operators living on the asymptotic boundary at the same instant. The existence of such a reconstruction is highly nontrivial and is conceptually puzzling if we think in terms of physically detecting a local bulk particle from the boundary of the AdS$_{d+1}$, as this signals a non-local information encoding scheme. In this paper, we explore situations where such non-locally encoded information can be observed in semiclassical gravity. We study examples where it is more efficient to utilize such effects in quantum gravity to detect a bulk excitation than to wait for signals to reach the boundary. Furthermore, we provide exemplified situations for which the protocol fails, and the non-locality of information is suppressed. These exemplified scenarios can be taken as explicit examples of the emergence of a perturbatively localized observer. In such cases, holography cannot be proven at the perturbative level in Newton's constant $G_{N}$ via the non-localizability of information.