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Holographic Entanglement Entropy

  • Mukund Rangamani
  • Tadashi Takayanagi
Book

Part of the Lecture Notes in Physics book series (LNP, volume 931)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Mukund Rangamani, Tadashi Takayanagi
    Pages 1-4
  3. Quantum Entanglement

    1. Front Matter
      Pages 5-5
    2. Mukund Rangamani, Tadashi Takayanagi
      Pages 7-26
    3. Mukund Rangamani, Tadashi Takayanagi
      Pages 27-32
  4. Holography and Entanglement

    1. Front Matter
      Pages 33-33
    2. Mukund Rangamani, Tadashi Takayanagi
      Pages 35-47
    3. Mukund Rangamani, Tadashi Takayanagi
      Pages 49-64
    4. Mukund Rangamani, Tadashi Takayanagi
      Pages 65-95
  5. Entanglement and Quantum Dynamics

    1. Front Matter
      Pages 97-97
    2. Mukund Rangamani, Tadashi Takayanagi
      Pages 99-123
    3. Mukund Rangamani, Tadashi Takayanagi
      Pages 125-143
    4. Mukund Rangamani, Tadashi Takayanagi
      Pages 145-154
    5. Mukund Rangamani, Tadashi Takayanagi
      Pages 155-164
  6. Quantum Gravity

    1. Front Matter
      Pages 165-165
    2. Mukund Rangamani, Tadashi Takayanagi
      Pages 167-169
    3. Mukund Rangamani, Tadashi Takayanagi
      Pages 171-183
    4. Mukund Rangamani, Tadashi Takayanagi
      Pages 185-220
    5. Mukund Rangamani, Tadashi Takayanagi
      Pages 221-234
  7. Back Matter
    Pages 235-246

About this book

Introduction

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.

Keywords

AdS/CFT Correspondence Gauge/Gravity Duality Tensor Networks CFT entanglement Entanglement first law Holographic first law Eternal black holes Quantum entanglement Holographic principle Quantum quenches Conformal Field Theory Quantum error correction Relative entropy Renormalization group Ferni surfaces Hyperscaling violation Gravity duals Vaidya-AdS

Authors and affiliations

  • Mukund Rangamani
    • 1
  • Tadashi Takayanagi
    • 2
  1. 1.Department of PhysicsUniversity of California, Center for Quantum Mathematics and PhysicsDavisUSA
  2. 2.Yukawa Institute for Theoretical Physics (YITP)Kyoto UniversityKyotoJapan

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-52573-0
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-52571-6
  • Online ISBN 978-3-319-52573-0
  • Series Print ISSN 0075-8450
  • Series Online ISSN 1616-6361
  • Buy this book on publisher's site
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