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

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 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.

Energy Reflection and Transmission at 2D Holographic Interfaces

“…This has been evaluated in a class of toy models where the black hole is coupled to a heat bath via transparent boundary conditions [44,45]. Holographic realizations corresponding to this scenario were put forward for example in [46][47][48][49][50] in terms of doubly holographic BCFT/ICFT models. Our results on reflection and transmission could come to use when coupling the black hole to the bath -we hope to return to this question in the future.…”

Gravity/Ensemble Duality

“…Beginning with Ref. [13], a number of interesting papers have explored the RT prescription for evaporating black holes in a "doubly holographic" setting [33][34][35][36][37]64]. The Hawking radiation is mainly carried by excitations of a holographic CFT d that escape to a (holographic) auxiliary system.…”

Replica wormholes for an evaporating 2D black hole

“…Penington [2] also gave some general arguments that the quantum extremal surface should exist for higher-dimensional black holes. In further work, the entropy formula has been applied to various other setups and it consistently produces a unitary Page curve [9,[12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] (see [29] for an introductory review).…”