The Fate of Information Localizability and Holography in Quantum Gravity

TL;DR

The paper investigates how locality and holography reconcile in AdS/CFT by constructing explicit boundary-based protocols to detect bulk excitations and by examining cases where such locality either holds approximately or fails due to gravitational constraints. It analyzes a gravity-assisted detection scheme that uses simple boundary operators and the ADM Hamiltonian to reveal bulk information on the same Cauchy slice, revealing a backreaction in the boundary time that can limit precision. It also develops several dressings of bulk operators—to background features, to clocks, or to entanglement—to show that perturbative locality can be compromised or restored depending on background structure, including in island-type setups with massive gravitons. The CFT perspective complements the bulk analysis by showing when multi-trace dressings can cancel singularities and enable bulk information localization, tying together boundary correlators, HKLL reconstruction, and state-dependent dressings. Overall, the work maps out a landscape where perturbative holography can be physically meaningful in some setups while being suppressed or altered in others, with implications for understanding islands and emergent observers 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.

Figures (7)

• Figure 1: An illustration of the particle detection measurement in global AdS$_{d+1}$. The white slice is a Cauchy slice in the bulk of AdS$_{d+1}$ and the gray ring is near its asymptotic boundary. A particle excitation, the orange wavepacket, is located at the center of a bulk Cauchy slice and an observer near the boundary at the same Cauchy slice, for example inside the gray ring, is trying to detect this particle.
• Figure 2: The probability distribution of the pointer location. Blue line denotes the initial probability distribution and the yellow line denotes the final probability distribution. The initial distribution only depends on the resolution of the detector which can be chosen to be arbitrarily small and this distribution is centered at $X=0$. The final distribution depends on the variance of $\hat{H}\hat{A}$, and can be large compared to $\sigma_X$. The probability that the detector detects an excitation approaches one as $\sigma_X$ approaches zero.
• Figure 3: The Penrose diagram of a large black hole in AdS formed from collapsing a matter shell. The shell's trajectory is in brown. We take two bulk points $P$ and $Q$ denoting bulk points in early time and late time respectively. The asymptotic time coordinate is denoted as $t$.
• Figure 4: The ratio $\frac{\langle\hat{\phi}_{\text{ref,s},I}(x,z)\hat{\phi}_{\text{ref,s},J}(x,z)\rangle}{\langle\hat{\phi}_{\text{ref,s},I}(x,z)\hat{\phi}_{\text{ref,s},I}(x,z)\rangle}$ with $\mu=0.4, k_{J,z}=15$ and $\vec{x}=0,z=5$. From this plot we can see that the ratio is extremely small if $k_{I,z}$ is away from $\pm k_{J,z}$ enough.
• Figure 5: The discrete plot of the ratio Equ. (\ref{['eq:rationfinal']}) with $\mu=0.4, \vec{y}=0$ and $\vec{x}=0,z=5$ as a function of $K$, the number of distilled modes, for the choices $k_{I,z}=\frac{2\pi}{5}(I+999)$ and $k_{I,z}=\frac{2\pi}{5}(I+4999)$ with $I=1,2,\cdots,K$. From the plot we can see that the ratio is getting closer to zero as we distill more modes or with the first mode having a higher energy.