Quantum Extremal Islands Made Easy, Part I: Entanglement on the Brane

TL;DR

This paper presents a simplified holographic framework demonstrating that quantum extremal islands naturally emerge in gravitational systems, extending their relevance beyond black holes to general effective theories of gravity.

Contribution

It introduces a holographic setup with a brane in AdS space where quantum extremal islands appear via the Ryu-Takayanagi prescription, showing their universality in gravity theories.

Findings

Quantum extremal islands arise when RT surfaces cross the brane.

Islands are shown to be a universal feature of effective gravity theories.

The framework connects entanglement entropy calculations to the presence of branes in AdS/CFT.

Abstract

Recent progress in our understanding of the black hole information paradox has lead to a new prescription for calculating entanglement entropies, which involves special subsystems in regions where gravity is dynamical, called \textit{quantum extremal islands}. We present a simple holographic framework where the emergence of quantum extremal islands can be understood in terms of the standard Ryu-Takayanagi prescription, used for calculating entanglement entropies in the boundary theory. Our setup describes a $d$-dimensional boundary CFT coupled to a ($d$-1)-dimensional defect, which are dual to global AdS${}_{d+1}$ containing a codimension-one brane. Through the Randall-Sundrum mechanism, graviton modes become localized at the brane, and in a certain parameter regime, an effective description of the brane is given by Einstein gravity on an AdS${}_d$ background coupled to two copies of the boundary CFT. Within this effective description, the standard RT formula implies the existence of quantum extremal islands in the gravitating region, whenever the RT surface crosses the brane. This indicates that islands are a universal feature of effective theories of gravity and need not be tied to the presence of black holes.