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 AdSd+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 AdSd 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.
Highlights
There, one expects that after an initial rise of the entanglement entropy of the Hawking radiation, subtle correlations between the quanta emitted at early and late times lead to a purification of the final state and a decrease in the late-time entropy
As emphasized with the generalized second law [15], the geometric BH entropy is naturally combined with the entanglement entropy of quantum fields outside the event horizon to produce a finite quantity known as the generalized entropy
The entropy of the radiation collected in a nongravitating reservoir is evaluated as the contributions from the quantum fields in the reservoir but possibly on a quantum extremal island (QEI) in the gravitating region, i.e., a separate region near the black hole, as well as a geometric BH contribution from the boundary of the island
Summary
As described in the introduction, we are studying a holographic system where the boundary theory is a d-dimensional CFT which lives on a spherical cylinder R × Sd−1 (where the R is the time direction) This CFT is coupled to a (codimension-one) conformal defect positioned on the equator of the sphere. The bulk description of this system involves an asymptotically AdSd+1 spacetime with a codimension-one brane spread through the middle of the space (and extending to the position of the defect at asymptotic infinity) In this setup, the brane has an AdSd geometry and further, we consider the case in which the brane has a substantial tension and backreacts on the bulk geometry. We review the bulk geometry produced by the backreaction of the brane, and the gravitational action induced on the brane
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