Geometrizing the partial entanglement entropy: from PEE threads to bit threads

Lin, Jiong1,2; Lu, Yizhou3; Wen, Qiang4,5

2024-02-23

10.1007/JHEP02(2024)191

JOURNAL OF HIGH ENERGY PHYSICS   影响因子和分区

1029-8479

We give a scheme to geometrize the partial entanglement entropy (PEE) for holographic CFT in the context of AdS/CFT. More explicitly, given a point x we geometrize the two-point PEEs between x and any other points in terms of the bulk geodesics connecting these two points. We refer to these geodesics as the PEE threads, which can be naturally regarded as the integral curves of a divergenceless vector field Vx mu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {V}_{\textbf{x}}<^>{\mu } $$\end{document}, which we call PEE thread flow. The norm of Vx mu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {V}_{\textbf{x}}<^>{\mu } $$\end{document} that characterizes the density of the PEE threads can be determined by some physical requirements of the PEE. We show that, for any static interval or spherical region A, a unique bit thread configuration can be generated from the PEE thread configuration determined by the state. Hence, the non-intrinsic bit threads are emergent from the intrinsic PEE threads. For static disconnected intervals, the vector fields describing a divergenceless flow is no longer suitable to reproduce the RT formula. We weight a PEE thread with the number of times it intersects with any homologous surface. Instead, the RT formula is perfectly reformulated by the minimization of the summation of PEE threads with all possible assignment of weights.

AdS-CFT Correspondence Gauge-Gravity Correspondence Models of Quantum Gravity

SCI

英语

其他

National Natural Science Foundation of China[12247161] ; NSFC Research Fund for International Scientists[12250410250] ; China Postdoctoral Science Foundation[2022TQ0140]

Physics

Physics, Particles & Fields

WOS:001169807700001

SPRINGER

PHYSICS

Web of Science

1.Univ Sci & Technol China, Interdisciplinary Ctr Theoret Study, 96 Jinzai Ave, Hefei 230026, Anhui, Peoples R China
2.Peng Huanwu Ctr Fundamental Theory, 96 Jinzai Ave, Hefei 230026, Anhui, Peoples R China
3.Southern Univ Sci & Technol, Dept Phys, 1088 Xueyuan Ave, Shenzhen 518055, Peoples R China
4.Southeast Univ, Shing Tung Yau Ctr, 2 Sipailou, Nanjing 210096, Peoples R China
5.Southeast Univ, Sch Phys, 2 Sipailou, Nanjing, Peoples R China

Lin, Jiong,Lu, Yizhou,Wen, Qiang. Geometrizing the partial entanglement entropy: from PEE threads to bit threads[J]. JOURNAL OF HIGH ENERGY PHYSICS,2024(2).

Lin, Jiong,Lu, Yizhou,&Wen, Qiang.(2024).Geometrizing the partial entanglement entropy: from PEE threads to bit threads.JOURNAL OF HIGH ENERGY PHYSICS(2).

Lin, Jiong,et al."Geometrizing the partial entanglement entropy: from PEE threads to bit threads".JOURNAL OF HIGH ENERGY PHYSICS .2(2024).