Defect Extremal Surface for Reflected Entropy

Abstract

Defect extremal surface is defined by extremizing the Ryu-Takayanagi formula corrected by the quantum defect theory. This is interesting when the AdS bulk contains a defect brane (or string). We introduce a defect extremal surface formula for reflected entropy, which is a mixed state generalization of entanglement entropy measure. Based on a decomposition procedure of an AdS bulk with a brane, we demonstrate the equivalence between defect extremal surface formula and island formula for reflected entropy in AdS${}_3$/BCFT${}_2$. We also compute the evolution of reflected entropy in evaporating black hole model and find that defect extremal surface formula agrees with island formula.

1+35 pages, 23 figures

References in corpus (19)

• Entanglement Entropy at Large Central Charge
• An Information Paradox and Its Resolution in de Sitter Holography
• Page Curve for an Evaporating Black Hole
• Islands in Asymptotically Flat 2D Gravity
• Gravity/Ensemble Duality
• Notes on islands in asymptotically flat 2d dilaton black holes
• Entanglement entropy in holographic moving mirror and Page curve
• Quantum Extremal Islands Made Easy, PartIII: Complexity on the Brane
• Islands and Page curves in 4d from Type IIB
• Islands in charged linear dilaton black holes
• Defect extremal surface as the holographic counterpart of Island formula
• Islands in Linear Dilaton Black Holes
• Multipartite Reflected Entropy
• Islands in the Stream of Hawking Radiation
• Entanglement island, miracle operators and the firewall
• Evaporation of black holes in flat space entangled with an auxiliary universe
• Evaporating Black Holes Coupled to a Thermal Bath
• Page Curve from Defect Extremal Surface and Island in Higher Dimensions
• The Universal Coefficient Theorem, Wormholes, and the Island

Cited by in corpus (11)

• Entanglement Phase Structure of a Holographic BCFT in a Black Hole Background
• The universality of islands outside the horizon
• BCFT in a Black Hole Background: An Analytical Holographic Model
• Entanglement Islands in Generalized Two-dimensional Dilaton Black Holes
• The Markov gap in the presence of islands
• JT Gravity from Partial Reduction and Defect Extremal Surface
• Defect extremal surfaces for entanglement negativity
• Reflected Entropy for Communicating Black Holes I: Karch-Randall Braneworlds
• Reflected Entropy and Entanglement Negativity for Holographic Moving Mirrors
• Entanglement Negativity and Defect Extremal Surface
• Entanglement wedge cross section inequalities in AdS/BCFT