Geometry and Entanglement in AdS/CFT and Beyond

Geometry and Entanglement in AdS/CFT and Beyond

Author: Chang-Han Chen (Researcher in physics)

Publisher:

Published: 2022

Total Pages: 0

ISBN-13:

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Holographic duality is the most well-understood non-perturbative framework of quantum gravity that we have. In particular, it has revealed a deep connection between quantum entanglement and the dual gravitational geometry. A semiclassical analysis on geometries has shed insights on the non-perturbative aspects of quantum field theories, some of which does not seem to require an asymptotic anti-de Sitter boundary. This raises the question, "What does the semiclassical gravity actually know, and how?" This thesis aims to approach a very narrow aspect of this question by, first, summarizing developments in the leading order perturbation theory. Then, we make some small advances on generalizing the perturbative framework to geometries beyond AdS/CFT. On the field theory we side, we discuss perturbation theory with irrelevant deformations; on the gravity side, we study cutoff AdS and D3 brane geometry. The result is not conclusive, but we believe that the framework we set up, along with knowledge in the first few chapters, will lead us to a better understanding of what the perturbation theory of semiclassical gravity is actually capable of.


AdS3/CFT2 and Holographic Entanglement Entropy

AdS3/CFT2 and Holographic Entanglement Entropy

Author: Jie-qiang Wu

Publisher: Springer Nature

Published: 2019-10-18

Total Pages: 145

ISBN-13: 9811332126

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This book focuses on AdS3/CFT2, addressing different aspects of this correspondence in field theory and in gravity, including entanglement entropy, higher genus partition function, and conformal block. Holographic entanglement entropy is an important area in holographic and quantum information, which implies a deep relation between geometry and quantum entanglement. In this book, the authors use holographic entanglement entropy as a tool to investigate AdS3/CFT2. They study the entanglement entropy at high temperature in field theory and in holographics, and show that the results match each other in classical and one-loop order. In the AdS3/CFT2 system, they examine in detail the correspondence, exploring the higher genus partition function, entanglement entropy in a general system and conformal block, and they find good correspondence in field theory and gravity. The result strongly supports AdS3/CFT2 correspondence. In addition, they develop several important techniques in 2d CFT and 3d gravity, which also offer inspiration for other fields.


From Gravity to Thermal Gauge Theories: The AdS/CFT Correspondence

From Gravity to Thermal Gauge Theories: The AdS/CFT Correspondence

Author: Eleftherios Papantonopoulos

Publisher: Springer

Published: 2011-03-27

Total Pages: 433

ISBN-13: 3642048641

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The AdS/CFT correspondence is a powerful tool in studying strongly coupled phenomena in gauge field theories, using results from a weakly coupled gravity background studied in the realm of string theory. AdS/CFT was first successfully applied to the study of phenomena such as the quark-gluon plasma produced in heavy ions collisions. Soon it was realized that its applicability can be extended, in a more phenomenological approach, to condensed matter systems and to systems described by fluid dynamics. The set of tutorial reviews in this volume is intended as an introduction to and survey of the principle of the AdS/CFT correspondence in its field/string theoretic formulation, its applicability to holographic QCD and to heavy ions collisions, and to give a first account of processes in fluid dynamics and condensed matter physics, which can be studied with the use of this principle. Written by leading researchers in the field and cast into the form of a high-level but approachable multi-author textbook, this volume will be of benefit to all postgraduate students, and newcomers from neighboring disciplines wishing to find a comprehensive guide for their future research.


Holographic Entanglement Entropy

Holographic Entanglement Entropy

Author: Mukund Rangamani

Publisher: Springer

Published: 2017-05-08

Total Pages: 245

ISBN-13: 3319525735

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This book provides a comprehensive overview of developments in the field of holographic entanglement entropy. Within the context of the AdS/CFT correspondence, it is shown how quantum entanglement is computed by the area of certain extremal surfaces. The general lessons one can learn from this connection are drawn out for quantum field theories, many-body physics, and quantum gravity. An overview of the necessary background material is provided together with a flavor of the exciting open questions that are currently being discussed. The book is divided into four main parts. In the first part, the concept of entanglement, and methods for computing it, in quantum field theories is reviewed. In the second part, an overview of the AdS/CFT correspondence is given and the holographic entanglement entropy prescription is explained. In the third part, the time-dependence of entanglement entropy in out-of-equilibrium systems, and applications to many body physics are explored using holographic methods. The last part focuses on the connection between entanglement and geometry. Known constraints on the holographic map, as well as, elaboration of entanglement being a fundamental building block of geometry are explained. The book is a useful resource for researchers and graduate students interested in string theory and holography, condensed matter and quantum information, as it tries to connect these different subjects linked by the common theme of quantum entanglement.


Introduction to the AdS/CFT Correspondence

Introduction to the AdS/CFT Correspondence

Author: Horaƫiu Năstase

Publisher: Cambridge University Press

Published: 2015-09-10

Total Pages: 457

ISBN-13: 1316352307

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Providing a pedagogical introduction to the rapidly developing field of AdS/CFT correspondence, this is one of the first texts to provide an accessible introduction to all the necessary concepts needed to engage with the methods, tools and applications of AdS/CFT. Without assuming anything beyond an introductory course in quantum field theory, it begins by guiding the reader through the basic concepts of field theory and gauge theory, general relativity, supersymmetry, supergravity, string theory and conformal field theory, before moving on to give a clear and rigorous account of AdS/CFT correspondence. The final section discusses the more specialised applications, including QCD, quark-gluon plasma and condensed matter. This book is self-contained and learner-focused, featuring numerous exercises and examples. It is essential reading for both students and researchers across the fields of particle, nuclear and condensed matter physics.


Beyond Spacetime

Beyond Spacetime

Author: Nick Huggett

Publisher: Cambridge University Press

Published: 2020-05-14

Total Pages: 371

ISBN-13: 110847702X

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A collection of essays discussing the philosophy and foundations of quantum gravity. Written by leading philosophers and physicists in the field, chapters cover the important conceptual questions in the search for a quantum theory of gravity, and the current state of understanding among philosophers and physicists.


AdS/CFT Duality User Guide

AdS/CFT Duality User Guide

Author: Makoto Natsuume

Publisher: Springer

Published: 2015-04-01

Total Pages: 299

ISBN-13: 4431554416

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This book describes applications of the AdS/CFT duality to the "real world." The AdS/CFT duality is an idea that originated from string theory and is a powerful tool for analyzing strongly-coupled gauge theories using classical gravitational theories. In recent years, it has been shown that one prediction of AdS/CFT is indeed close to the experimental result of the real quark–gluon plasma. Since then, the AdS/CFT duality has been applied to various fields of physics; examples are QCD, nuclear physics, condensed-matter physics, and nonequilibrium physics. The aim of this book is to provide background materials such as string theory, black holes, nuclear physics, condensed-matter physics, and nonequilibrium physics as well as key applications of the AdS/CFT duality in a single volume. The emphasis throughout the book is on a pedagogical and intuitive approach focusing on the underlying physical concepts. It also includes step-by-step computations for important results, which are useful for beginners. This book will be a valuable reference work for graduate students and researchers in particle physics, general relativity, nuclear physics, nonequilibrium physics, and condensed-matter physics.


Gauge/Gravity Duality

Gauge/Gravity Duality

Author: Martin Ammon

Publisher: Cambridge University Press

Published: 2015-04-09

Total Pages: 549

ISBN-13: 1107010349

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The first textbook on this important topic, for graduate students and researchers in particle and condensed matter physics.


Philosophy Beyond Spacetime

Philosophy Beyond Spacetime

Author: Christian Wüthrich

Publisher: Oxford University Press

Published: 2021-08-26

Total Pages: 288

ISBN-13: 019258247X

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Quantum gravity seeks a unified theory in which quantum matter is dynamically related to generally relativistic spacetime. Although a continuing work in progress, research programmes in the field such as string theory, loop quantum gravity, and causal set theory make it clear that a successful theory of quantum gravity will raise important challenges to our conceptions of space, time, and matter-perhaps abolishing them altogether as fundamental entities. But just as important, there is good reason to think that some of the problems in finding a theory of quantum gravity are themselves conceptual, in need of philosophical analysis. Philosophy Beyond Spacetime: Implications from Quantum Gravity assembles original papers from philosophers (and one physicist), establishing a definitive statement of the current state of play, on which future research into this area can build. Aiming to expand knowledge and understanding of the philosophy of quantum gravity, it emphasizes how debates in metaphysics—regarding emergence, composition, or grounding for example—shed light on the conceptual questions of quantum gravity. And conversely, how quantum theories of space and time call into question philosophical views grounded in classical spacetime. Furthermore, the philosophy of quantum gravity raises methodological questions, for instance concerning the relation between physics and metaphysics. The essays have been chosen to demonstrate to a wide range of philosophers the significance of the subject, as well as making novel contributions to it.


Holographic Quantum Matter

Holographic Quantum Matter

Author: Sean A. Hartnoll

Publisher: MIT Press

Published: 2018-03-16

Total Pages: 407

ISBN-13: 0262348020

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A comprehensive overview of holographic methods in quantum matter, written by pioneers in the field. This book, written by pioneers in the field, offers a comprehensive overview of holographic methods in quantum matter. It covers influential developments in theoretical physics, making the key concepts accessible to researchers and students in both high energy and condensed matter physics. The book provides a unique combination of theoretical and historical context, technical results, extensive references to the literature, and exercises. It will give readers the ability to understand the important problems in the field, both those that have been solved and those that remain unsolved, and will enable them to engage directly with the current literature. The book describes a particular interface between condensed matter physics, gravitational physics, and string and quantum field theory made possible by holographic duality. The chapters cover such topics as the essential workings of the holographic correspondence; strongly interacting quantum matter at a fixed commensurate density; compressible quantum matter with a variable density; transport in quantum matter; the holographic description of symmetry broken phases; and the relevance of the topics covered to experimental challenges in specific quantum materials. Holographic Quantum Matter promises to be the definitive presentation of this material.