Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Massive Islands

Hao Geng, Andreas Karch

TL;DR

The paper investigates how graviton mass, induced by transparent boundary conditions in AdS/BCFT/RS setups, influences the formation of entanglement islands and the Page curve in higher dimensions. It provides an analytically tractable model using an N=4 SYM orbifold BCFT dual, demonstrating islands persist in a massive-graviton regime and can dominate radiation entropy. In the massless-graviton limit, islands disappear, suggesting the graviton mass is crucial for island physics in these holographic settings. The work connects RS brane gravity, BCFT operator structure, and holographic entanglement entropy to clarify when semi-classical island calculations are reliable in higher dimensions.

Abstract

We comment on the role of the graviton mass in recent calculations of the Page curve using holographic ideas. All reliable calculations of the Page curve in more than 2+1 spacetime dimensions have been performed in systems with massive gravitons. A crucial ingredient in these calculations is the formation of islands, regions that contribute to the entropy of degrees of freedom located elsewhere. While most often simply ignored, it is indeed true that mass of the graviton does not appear to significantly affect the calculations that appeared in the literature. We use the freedom to change the graviton mass to give an extremely simple model of analytically tractable island formation in general dimensions. We do however note that if one attempts to take the limit of zero graviton mass, any contribution from the islands disappears. This raises the question to what extent entanglement islands can play a role in standard massless gravity.

Massive Islands

TL;DR

The paper investigates how graviton mass, induced by transparent boundary conditions in AdS/BCFT/RS setups, influences the formation of entanglement islands and the Page curve in higher dimensions. It provides an analytically tractable model using an N=4 SYM orbifold BCFT dual, demonstrating islands persist in a massive-graviton regime and can dominate radiation entropy. In the massless-graviton limit, islands disappear, suggesting the graviton mass is crucial for island physics in these holographic settings. The work connects RS brane gravity, BCFT operator structure, and holographic entanglement entropy to clarify when semi-classical island calculations are reliable in higher dimensions.

Abstract

We comment on the role of the graviton mass in recent calculations of the Page curve using holographic ideas. All reliable calculations of the Page curve in more than 2+1 spacetime dimensions have been performed in systems with massive gravitons. A crucial ingredient in these calculations is the formation of islands, regions that contribute to the entropy of degrees of freedom located elsewhere. While most often simply ignored, it is indeed true that mass of the graviton does not appear to significantly affect the calculations that appeared in the literature. We use the freedom to change the graviton mass to give an extremely simple model of analytically tractable island formation in general dimensions. We do however note that if one attempts to take the limit of zero graviton mass, any contribution from the islands disappears. This raises the question to what extent entanglement islands can play a role in standard massless gravity.

Paper Structure

This paper contains 7 sections, 14 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Massive RS Gravity
  3. Islands and black holes
  4. Analytic construction of islands for a ${\cal N}=4$ SYM based AdS/BCFT pair
  5. Islands from equilibrium
  6. The minimal massive island model
  7. Massless Gravitons

Figures (2)

  • Figure 1: Embedding of subcritical RS branes in anti-de Sitter space and in the planar AdS Schwarzschild. R denotes the region whose entanglement entropy we wish to calculate, and the dashed green lines connected to the boundary of R are the two candidate RT surfaces.
  • Figure 2: Area difference $\Delta A$ as a function of $y_0$ in units where $z_h^{-1} = \pi T =1$.