Page Curve from Defect Extremal Surface and Island in Higher Dimensions

Abstract

Defect extremal surface is defined by minimizing the Ryu-Takayanagi surface corrected by the defect theory, which is useful when the RT surface crosses or terminates on the defect. Based on the decomposition procedure of a AdS bulk with a defect brane, proposed in arXiv:2012.07612, we derive Page curve in a time dependent set up of AdS${}_3$/BCFT${}_2$, and find that the result from island formula agrees with defect extremal surface formula precisely. We then extend the study to higher dimensions and find that the entropy computed from bulk defect extremal surface is generally less than that from island formula in boundary low energy effective theory, which implies that the UV completion of island formula gives a smaller entropy in higher dimensions.

45 pages, 18 figures

References in corpus (13)

• Entanglement Entropy at Large Central Charge
• Page Curve for an Evaporating Black Hole
• Islands in Asymptotically Flat 2D Gravity
• Gravity/Ensemble Duality
• Entanglement entropy in holographic moving mirror and Page curve
• Notes on islands in asymptotically flat 2d dilaton black holes
• Quantum Extremal Islands Made Easy, PartIII: Complexity on the Brane
• Defect extremal surface as the holographic counterpart of Island formula
• Islands in Linear Dilaton Black Holes
• Coarse-Graining Holographic States: A Semiclassical Flow in General Spacetimes
• Evaporating Black Holes Coupled to a Thermal Bath
• Concerns about the replica wormhole derivation of the island conjecture
• A 2-Replica Wormhole