Defect extremal surfaces for entanglement negativity

Abstract

We propose a doubly holographic version of the semi-classical island formula for the entanglement negativity in the framework of the defect AdS/BCFT correspondence where the AdS bulk contains a defect conformal matter theory. In this context, we propose a defect extremal surface (DES) formula for computing the entanglement negativity modified by the contribution from the defect matter theory on the end-of-the-world brane. The equivalence of the DES proposal and the semi-classical island formula for the entanglement negativity is demonstrated in AdS${}_3$/BCFT${}_2$ framework. Furthermore, in the time-dependent AdS${}_3$/BCFT${}_2$ scenarios involving eternal black holes in the lower dimensional effective description, we investigate the time evolution of the entanglement negativity through the DES and the island formulae and obtain the analogues of the Page curves.

45 pages, 25 figures

References in corpus (35)

• Entanglement negativity in quantum field theory
• Finite temperature entanglement negativity in conformal field theory
• Page Curve for an Evaporating Black Hole
• Islands in Asymptotically Flat 2D Gravity
• 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
• Entanglement Phase Structure of a Holographic BCFT in a Black Hole Background
• Comments on Entanglement Negativity in Holographic Field Theories
• Conformal Blocks and Negativity at Large Central Charge
• Quantum Extremal Islands Made Easy, Part IV: Massive Black Holes on the Brane
• Defect extremal surface as the holographic counterpart of Island formula
• Islands in Linear Dilaton Black Holes
• Sailing past the End of the World and discovering the Island
• Reflected entropy in random tensor networks
• Island, Page Curve and Superradiance of Rotating BTZ Black Holes
• The Page Curve for Reflected Entropy
• Balanced Partial Entanglement and Mixed State Correlations
• Entanglement negativity, reflected entropy, and anomalous gravitation
• AdS/BCFT and Island for curvature-squared gravity
• Islands in Closed and Open Universes
• Page Curve of Effective Hawking Radiation
• Information transfer with a twist
• Microcanonical Action and the Entropy of Hawking Radiation
• Page Curves of Reissner-Nordström Black Hole in HD Gravity
• Grey-body Factors, Irreversibility and Multiple Island Saddles
• Page curve from dynamical branes in JT gravity
• Islands and the de Sitter entropy bound
• Reflected Entropy and Entanglement Negativity for Holographic Moving Mirrors
• Spontaneous Radiation of Black Holes
• Page Curve from Defect Extremal Surface and Island in Higher Dimensions
• Holographic moving mirrors
• Retrieving black hole information from the main Lorentzian saddle point
• The Markov gap for geometric reflected entropy
• On the assumptions leading to the information loss paradox

Cited by in corpus (9)

• Entanglement entropy analysis of dyonic black holes using doubly holographic theory
• End of the World Brane meets $T\bar{T}$
• Reflected entropy in BCFTs on a black hole background
• Islands and dynamics at the interface
• Holographic Reflected Entropy and Islands in Interface CFTs
• Page Curve of AdS-Vaidya Model for Evaporating Black Holes
• Bridging Boundaries: $T\bar{T}$, Double Holography, and Reflected Entropy
• Binary AdS black holes coupled to a bath in Type IIB
• Entanglement Negativity and Defect Extremal Surface