The Mechanism behind the Information Encoding for Islands

TL;DR

The paper tackles how information inside entanglement islands is nonlocally encoded in a disconnected bath within holographic island models. It identifies a universal mechanism: in massive gravity (the island Higgs phase), island operators are dressed to the bath through a nonperturbative coupling that yields a nonzero commutator with the bath Hamiltonian, enabling bath-dressing of island observables. The authors develop both a weakly coupled explicit island model and a holographic Karch-Randall braneworld toy model to show this dressing via gravitational Wilson lines and Stückelberg vector fields, and they demonstrate consistency with entanglement wedge reconstruction. The results connect island holography to ER=EPR by geometrizing the dressing as extra-dimensional Wilson lines, suggesting a general, state-aware mechanism for information encoding in gravitational systems with potential broader implications for the black hole information problem.

Abstract

Entanglement islands are subregions in a gravitational universe whose information is fully encoded in a disconnected non-gravitational system away from it. In the context of the black hole information paradox, entanglement islands state that the information about the black hole interior is encoded in the early-time Hawking radiation. Nevertheless, it was unclear how this seemingly nonlocal information encoding emerges from a manifestly local theory. In this paper, we provide an answer to this question by uncovering the mechanism behind this information encoding scheme. As we will see, the early understanding that graviton is massive in island models plays an essential role in this mechanism. As an example, we will discuss how this mechanism works in detail in the Karch-Randall braneworld. This study also suggests the potential importance of this mechanism to the ER=EPR conjecture.

Figures (6)

• Figure 1: a) The Penrose diagram of the island model with a black in the AdS$_{d+1}$. The two red vertical lines denotes the conformal boundary of the AdS$_{d+1}$ black hole. The green shaded regions are the nongravitational bath whose geometry is the flat Minkowski space. The orange arrows denotes the radiation coming in and out of the black hole. Under the time evolution chosen in the diagram, more and more radiation from the black hole will be captured by the bath. Two Cauchy slices of this time evolution are denoted by the two blue curves and on each of them we specify the subsystem $R=R_{I}\cup R_{II}$ as the red intervals. b) A putative configuration with entanglement island. The island is denoted as the purple interval in the black hole spacetime. The causal diamond of the island overlaps the black hole interior which is the reason the interior of the black hole is encoded in the bath.
• Figure 2: We couple the gravitational AdS$_{d+1}$ universe (the blue shaded region) with a nongravitational bath (the green shaded region) by gluing them along the asymptotic boundary the of AdS$_{d+1}$ (the red vertical line). The nongravitational bath is modeled by another AdS$_{d+1}$ which shares the same asymptotic boundary with the original AdS$_{d+1}$. We take the Poincaré coordinates in both of the AdS$_{d+1}$. The coupling is achieved as described by Equ. (\ref{['eq:asympcouple']}).
• Figure 3: A constant time slice of an AdS$_{d+1}$ with a Karch-Randall brane. The green surface denotes the brane and it has AdS$_{d}$ geometry. All the dashed straight lines are in fact legitimate places for the brane to reside with the specific slice selected according to the brane tension Geng:2023qwm. The grey-shaded region behind the brane is cutoff. The red dot is the asymptotic boundary of the brane which is also called the defect in the literature. The defect lives at the end of the leftover asymptotic boundary (the thick black line) of the bulk.
• Figure 4: A demonstration of the construction of entanglement island in the Karch-Randall braneworld. The orange line denotes the bath subregion $R$ and the blue region on the brane denotes the island $\mathcal{I}$. The red surface $\gamma$ connecting $\partial R$ and $\partial\mathcal{I}$ is a minimal area surface called the Ryu-Takayanagi surface. $\gamma$ is determined by minimizing its area also with respect to its ending point $\partial \mathcal{I}$ on the brane which correspondence to the $\min_{ \mathcal{I}}$ in the island formula Equ. (\ref{['eq:islandformula']}).
• Figure 5: A demonstration of the dressing using the Wilson line $\theta(x,\rho)$. The cross denotes the operator insertion at $(x,\rho)$ and the wavy curve connecting the cross to the asymptotic boundary denotes the Wilson line. This Wilson line can end at any point on the asymptotic boundary