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Traversable Wormholes and Regenesis The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Gao, Ping. 2019. Traversable Wormholes and Regenesis. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences. Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:42029626 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA Traversable Wormholes and Regenesis A dissertation presented by Ping Gao to The Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of Physics Harvard University Cambridge, Massachusetts April 2019 c 2019 | Ping Gao All rights reserved. Dissertation Advisor: Daniel Louis Jafferis Ping Gao Traversable Wormholes and Regenesis Abstract In this dissertation we study a novel solution of traversable wormholes in the context of AdS/CFT. This type of traversable wormhole is the first such solution that has been shown to be embeddable in a UV complete theory of gravity. We discuss its property from points of view of both semiclassical gravity and general chaotic system. On gravity side, after turning on an interaction that couples the two boundaries of an eternal BTZ black hole, in chapter 2 we find a quantum matter stress tensor with negative average null energy, whose gravitational backreaction renders the Einstein-Rosen bridge traversable. Such a traversable wormhole has an interesting interpretation in the context of ER=EPR, which we suggest might be related to quantum teleportation. However, it cannot be used to violate causality. We also discuss the implications for the energy and holographic entropy in the dual CFT description. The gravity solution of this traversable wormhole indicates that in holographic systems signals generated by a source could reappear long after they have dissipated, with the need of only performing some simple operations. In chapter 3, we argue the phenomenon, to which we refer as \regenesis", is universal in general quantum chaotic many-body systems, and elucidate its underlying physics. The essential elements behind the phenomenon are: (i) scrambling which in a chaotic system makes out-of-time-ordered correlation functions (OTOCs) vanish at large times; (ii) the entanglement structure of the state of the system. The latter aspect also implies that the regenesis phenomenon requires fine tuning of the initial state. Compared to other manifestations of quantum chaos such as the initial growth of OTOCs which deals with early times, and a random matrix-type energy spectrum which reflects very large time behavior, regenesis concerns with intermediate times, of order the scrambling time of a system. We also study the phenomenon in detail in general two-dimensional conformal field theories in the large central charge limit, and highlight some interesting features including a resonant enhancement of regenesis signals near the scrambling time and their oscillations in coupling. Finally, we discuss gravity implications of the phenomenon for systems with a gravity dual, arguing that there exist regimes for which traversability of a wormhole is quantum in nature, i.e. cannot be associated with a semi-classical spacetime causal structure. iii iv Contents Abstract iii Citations to previously published work viii Acknowledgments ix Dedication xi 1 Introduction and Summary1 2 Traversable Wormholes via a Double Trace Deformation7 2.1 Introduction....................................7 2.2 Modified bulk two-point function........................ 12 2.3 1-loop stress tensor................................ 15 2.4 Holographic Energy and Entropy........................ 20 2.5 Discussion..................................... 23 R 2.A dUTUU ...................................... 29 3 Regenesis and Quantum Traversable Wormholes 33 3.1 Introduction.................................... 33 3.2 A general argument for the regenesis phenomenon............... 39 v CONTENTS 3.2.1 More on the general setup........................ 39 3.2.2 Entanglement structure......................... 40 3.2.3 Regenesis behavior for quantum chaotic systems............ 41 3.2.4 Quantum nature of the regenesis signal................. 44 3.2.5 Robustness of the regenesis phenomenon................ 46 3.2.6 A contrast study: \regenesis" in a qubit model............. 48 3.2.7 A generalization: regenesis between spatially separated points.... 51 3.3 Explicit computations in large c CFTs..................... 51 3.3.1 Some useful expressions......................... 52 3.3.2 More elaborations on W ......................... 53 3.3.3 Evaluating W : part I........................... 53 3.3.4 Evaluating W : part II.......................... 56 3.4 Analysis of the results.............................. 57 3.4.1 General remarks............................. 57 3.4.2 A scaling limit.............................. 60 3.4.3 Three regimes of GLR ........................... 61 3.4.4 Multiple channel from integration.................... 63 3.4.5 Robustness of regenesis from CFT calculations............. 65 3.5 Gravity interpretation.............................. 66 3.5.1 Explicit comparison with gravity results................ 68 3.5.2 A semi-classical regime.......................... 70 3.5.3 Old cats never die............................. 72 3.5.4 Quantum traversable wormholes..................... 72 3.6 Discussions and future directions........................ 75 3.A Linear responses.................................. 77 vi CONTENTS 3.B An identity.................................... 79 3.C Details of CFT calculation............................ 80 3.C.1 Approximation of identity Virasoro block by conformal transformation 80 3.C.2 Application to W ............................. 84 3.C.3 Explicit expression of A ......................... 85 3.D Full k-dependence in multiple operator species................. 87 3.E Robustness of regenesis.............................. 93 References 99 vii Citations to previously published work Most of this thesis has appeared in print elsewhere. Details for particular chapters are given below. Chapter 2 • Gao, Ping, Daniel Louis Jafferis, and Aron C. Wall. \Traversable wormholes via a double trace deformation." Journal of High Energy Physics 2017.12 (2017): 151. arXiv:1608.05687 Chapter 3 • Gao, Ping, and Hong Liu. \Regenesis and quantum traversable wormholes." arXiv:1810.01444 Electronic preprints (shown in typewriter font) are available on the Internet at the following URL: http://arXiv.org viii Acknowledgments Six-year PhD student life in Harvard is a memorable time, in which I got to know the frontier of physics, started to build up my own research, and had wonderful experiences with many great people, to whom I would like to say \Thank you!" I am deeply grateful to my advisor Prof. Daniel Louis Jafferis. In past six years, he taught me how to think about problems with clear physical intuition. He is brilliant and always has special insight on many seemingly well understood problems. I was often amazed by his ability to capture the essence of problems, which might take me quite a long time of computation to obtain, within just a few lines of simple calculations or some elegant physical argument. Working with him inspired me to try thinking problems in various angles. I believe his insight, taste and enthusiasm towards physics will continue to affect my research in the future. He is a very supportive advisor that he was always optimistic and encouraging me to find a way out whenever I fell into the swamp of complicated calculation and felt frustrated. I specially thank Daniel for guiding me to the project on traversable wormholes, which is the main topic of this thesis. It raises my strong and long-term interest in the interface between quantum gravity, quantum many-body system and quantum information. I would also like to express my gratitude to Prof. Hong Liu. I was impressed by his clear and pedagogically excellent lecture on holographic duality, which helped me understanding this grand topic in a short time. Besides the help in class, I am also grateful for his guidance, stimulating discussions and insightful comments in our collaborations on effective field theory of hydrodynamics and regenesis. He has a strong intuition in finding an elegant and simple physical interpretation behind complicated calculation, which affects my way of thinking on physics. Thanks to my committee members: Prof. Andy Strominger and Prof. Melissa Franklin. They gave me useful feedback on my research process. In particular, I want to single out Andy for his excellent course on black holes that is very beneficial to my understanding on quantum gravity. Moreover, I must express my gratitude to many other professors who taught a course I took or sat in. I have taken Prof. Xi Yin's super well-organzied courses on string theory and CFT, that built up my foundamental knowledge in these areas. I have enjoyed many mathematical courses by Hiro Lee Tanaka, Hector Pasten, Jonathan Mboyo Esole and Prof. Curt McMullen. I am quite impressed by the elegance of mathematics, though it still requires more time for me to gain applicable insight from it. ix CHAPTER 0. ACKNOWLEDGMENTS Thanks to Logan McCarty, Louis Deslauriers, Prof. Daniel Louis Jafferis and Prof. Gerald Gabrielse for giving me opportunities
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