The Fate of Information Localizability and Holography in Quantum Gravity

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.