邊界共形場論之全像熵不等式｜國立清華大學博碩士論文庫

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研究生：	林柏翰 Lin, Bo-Han
論文名稱：	邊界共形場論之全像熵不等式 Holographic Entropy Inequalities in Boundary Conformal Field Theory
指導教授：	朱創新 Chu, Chong-Sun 楊毅 Yang, Yi
口試委員:	溫文鈺 Wen, Wen-Yu 林豐利 Lin, Feng-Li
學位類別：	碩士 Master
系所名稱：	理學院 - 物理學系 Department of Physics
論文出版年：	2021
畢業學年度：	109
語文別：	英文
論文頁數：	57
中文關鍵詞：	反德西特/共形場論對偶、全像糾纏熵、全像邊界共行場論、全像熵不等式
外文關鍵詞：	AdS/CFT correspondence, Holographic entanglement entropy, Holographic BCFT, Holographic entropy inequalities
相關次數：	點閱：2 下載：0
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本文利用反德西特/共形場論對偶分析邊界共形場論中的全像熵不等式。藉由全像熵在不同溫度的相圖，我們得以分類所有可能出現的組態，並進一步驗證在零溫及有限溫度時，全像熵不等式皆成立。

In this thesis, we study entropy inequalities in boundary conformal field theory by the AdS/CFT correspondence. By carefully classifying all the configurations for different phases, we verify the strong subadditivity and the monogamy of mutual information in the holographic dual of boundary conformal field theory at both zero and finite temperatures.

Introduction 1
Holographic Principle 2
1 Finite Temperature Field Theory . . . . . . . . . . . . . . . . . . . 2
2 Black Hole Temperature and Entropy . . . . . . . . . . . . . . . . . 3
3 AdS/CFT Correspondence . . . . . . . . . . . . . . . . . . . . . . . 4
Holographic Entanglement Entropy 6
1 Entanglement in Various Systems . . . . . . . . . . . . . . . . . . . 6
1.1 Entanglement in Bipartite Systems . . . . . . . . . . . . . . 6
1.2 Entanglement in Lattice Systems . . . . . . . . . . . . . . . 7
1.3 Entanglement in Quantum Field Theory . . . . . . . . . . . 8
2 Properties of Entanglement Entropy . . . . . . . . . . . . . . . . . . 8
2.1 UV Divergence of Entanglement Entropy . . . . . . . . . . . 8
2.2 Entropy Inequalities . . . . . . . . . . . . . . . . . . . . . . 9
3 The Ryu-Takayanagi Formula . . . . . . . . . . . . . . . . . . . . . 9
4 Properties of Holographic Entanglement Entropy . . . . . . . . . . 10
4.1 UV Divergence of Holographic Entanglement Entropy . . . . 10
4.2 Holographic Entropy Inequalities . . . . . . . . . . . . . . . 11
Holographic Entropy Inequalities in BCFT 15
1 Holographic BCFT . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 Holographic Entanglement Entropy . . . . . . . . . . . . . . . . . . 17
2.1 Pure AdS Spacetime . . . . . . . . . . . . . . . . . . . . . . 18
2.2 Schwarzschild-AdS Black Hole Background . . . . . . . . . . 20
3 Multipartite Systems in the Holographic BCFT . . . . . . . . . . . 22
3.1 Notations for Multipartite Systems . . . . . . . . . . . . . . 24
3.2 Rules for the Phase Diagram . . . . . . . . . . . . . . . . . . 25
3.3 Subadditivity . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4 Strong Subadditivity . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.1 Pure AdS spacetime . . . . . . . . . . . . . . . . . . . . . . 28
4.2 Schwarzschild-AdS Black Hole Background . . . . . . . . . . 32
5 Monogamy of Mutual Information . . . . . . . . . . . . . . . . . . . 32
5.1 Pure AdS spacetime . . . . . . . . . . . . . . . . . . . . . . 33
5.2 Schwarzschild-AdS Black Hole Background . . . . . . . . . . 37
Summary and Outlook 39
Appendices 40
A AdS Spacetime 40
A.1 Pure AdS Spacetime . . . . . . . . . . . . . . . . . . . . . . . . . . 40
A.2 Schwarzschild-AdS Black Hole Background . . . . . . . . . . . . . . 41
B Entanglement Entropy in CFT2 43
B.1 Vacuum State of CFT2 on R1;1 . . . . . . . . . . . . . . . . . . . . 43
B.2 Vacuum State of CFTd+1 on Rd,1 . . . . . . . . . . . . . . . . . . . 45
B.3 Thermal State of CFTd+1 on Rd,1 . . . . . . . . . . . . . . . . . . . 47
B.4 Vacuum State of CFT2 on S1  R . . . . . . . . . . . . . . . . . . . 50
B.5 Thermal State of CFT2 on S1  R . . . . . . . . . . . . . . . . . . 51

                                

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