Graviton Mass and Entanglement Islands in Low Spacetime Dimensions

TL;DR

The work investigates whether entanglement islands can coexist with long-range gravity by coupling a gravitational bulk to a nongravitational bath and formulating a unified description of gravitational Gauss' law violation. It develops a Stückelberg-based mechanism that generates a graviton mass term $M^{2}$ even when the bulk graviton lacks a tree-level propagator, thereby modifying Gauss' law. Focusing on (1+1)-D JT gravity, it shows that the bath-induced mass hides bulk energy from near-boundary observers, making islands compatible with gravity in this setting. The results suggest a universal link between entanglement islands and massive gravity across dimensions, with possible extensions to higher-spin cases and a practical method to compute $M^{2}$ from stress-tensor correlators.

Abstract

It has been conjectured and proven that entanglement island is not consistent with long-range (massless) gravity in a large class of spacetimes, including typical asymptotically anti-de Sitter spacetimes, in high spacetime dimensions. The conjecture and its proof are motivated by the observation that existing constructions of entanglement islands in high dimensions are all in gravitational theories where the graviton is massive for which the standard gravitational Gauss' law doesn't apply. In this letter, we show that this observation persists to lower dimensional cases. We achieve this goal by providing a unified description of the gravitational Gauss' law violation in island models that can work in any dimensions. This unified description teaches us new lessons on entanglement islands and subregion physics in quantum gravity. We focus on the case of the (1+1)-dimensional Jackiw-Teitelboim (JT) gravity for the purpose of demonstration.

Figures (2)

• Figure 1: We couple the gravitational AdS$_{d+1}$ with a nongravitational bath by gluing them along the asymptotic boundary the AdS$_{d+1}$. The bath is modeled by a CFT$_{d+1}$ living on a half Minkowski space sharing the same boundary as the asymptotic boundary of the AdS$_{d+1}$.
• Figure 2: The demonstration of the island calculation in Almheiri:2019yqk. We draw a Penrose diagram of the set-up where the red shaded region is the bulk AdS$_{2}$ described by geometry Equ. (\ref{['eq:poincare']}), the blue shaded region is the bath whose geometry is half of a 2d Minkowski space and the bath is glued to the bulk along the thick red vertical line ($x=0$). The pink causal diamond in the bath models the radiation $\mathcal{R}$ and the green causal diamond in the AdS$_{2}$ is the island $\mathcal{I}$ of $\mathcal{R}$. The physics in the island should be independent of that in the orange diamond.