Entanglement islands and cutoff branes from path-integral optimization

• Published in: The journal of high energy physics Vol. 2024; no. 7; pp. 69 - 41
• Main Authors: Chandra, Ashish, Li, Zhengjiang, Wen, Qiang
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 09.07.2024; Springer Nature B.V; SpringerOpen
• Subjects: AdS-CFT Correspondence; Black holes; Branes; Classical and Quantum Gravitation; Elementary Particles; Entanglement; Entropy; Gauge-Gravity Correspondence; Gravity; Holography; Models of Quantum Gravity; Optimization; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Radiation; Regular Article - Theoretical Physics; Relativity Theory; String Theory; AdS-CFT Correspondence; Gauge-Gravity Correspondence; Models of Quantum Gravity
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP07(2024)069

A bstract Recently it was proposed that, the AdS/BCFT correspondence can be simulated by a holographic Weyl transformed CFT 2 , where the cut-off brane plays the role of the Karch-Randall (KR) brane [ 1 ]. In this paper, we focus on the Weyl transformation that optimizes the path integral computation of the reduced density matrix for a single interval in a holographic CFT 2 . When we take the limit that one of the endpoint of the interval goes to infinity (a half line), such a holographic Weyl transformed CFT 2 matches the AdS/BCFT configuration for a BCFT with one boundary. Without taking the limit, the induced cutoff brane becomes a circle passing through the two endpoints of the interval. We assume that the cutoff brane also plays the same role as the KR brane in AdS/BCFT, hence the path-integral-optimized purification for the interval is in the island phase. This explains the appearance of negative mutual information observed in [ 2 ]. We check that, the entanglement entropy and the balanced partial entanglement entropy (BPE) calculated via the island formulas, exactly match with the RT formula and the entanglement wedge cross-section (EWCS), which are allowed to anchor on the cutoff brane.