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Author: Mukund Rangamani Publisher: Springer ISBN: 3319525735 Category : Science Languages : en Pages : 245
Book Description
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.
Author: Mukund Rangamani Publisher: Springer ISBN: 3319525735 Category : Science Languages : en Pages : 245
Book Description
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.
Author: Jie-qiang Wu Publisher: Springer ISBN: 9789811332111 Category : Science Languages : en Pages : 0
Book Description
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.
Author: Horaƫiu Năstase Publisher: Cambridge University Press ISBN: 1316352307 Category : Science Languages : en Pages : 457
Book Description
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.
Author: Dénes Petz Publisher: Springer Science & Business Media ISBN: 3540746366 Category : Science Languages : en Pages : 221
Book Description
This concise and readable book addresses primarily readers with a background in classical statistical physics and introduces quantum mechanical notions as required. Conceived as a primer to bridge the gap between statistical physics and quantum information, it emphasizes concepts and thorough discussions of the fundamental notions and prepares the reader for deeper studies, not least through a selection of well chosen exercises.
Author: Jude Currivan Publisher: Simon and Schuster ISBN: 1620556618 Category : Body, Mind & Spirit Languages : en Pages : 332
Book Description
How holographic patterns of information underlie our physical reality • 2017 Nautilus Silver Award • Includes myriad evidence from a wide range of cutting-edge scientific discoveries showing our Universe is an interconnected hologram of information • Explains how consciousness is a major component of the cosmic hologram of information, making us both manifestations and co-creators of our reality • Reconciles Quantum Mechanics and Einstein’s Theory of Relativity by showing that energy-matter and space-time are complementary expressions of information Our understanding of the Universe is about to transform at all levels, from the tiniest Planck scale to the vast reaches of space. Recent scientific discoveries show that the information that upholds all of our modern technologies is exactly the same as the universal in-formation that underpins, pervades, and is all we call physical reality. Exploring how information is more fundamental than energy, matter, space, or time, Jude Currivan, Ph.D., examines the latest research across many fields of study and many scales of existence to show how our Universe is in-formed and holographically manifested. She explains how the fractal in-formational patterns that guide behavior at the atomic level also guide the structure of galactic clusters in space. She demonstrates how the in-formational relationships that underlie earthquakes are the same as those that play out during human conflicts. She shows how cities grow in the same in-formational ways that galaxies evolve and how the dynamic in-formational forms that pervade ecosystems are identical to the informational structures of the Internet and our social behaviors. Demonstrating how information is physically real, the author explores how consciousness connects us to the many interconnected layers of universal in-formation, making us both manifestations and co-creators of the cosmic hologram of reality. She explains how Quantum Mechanics and Einstein’s Theory of Relativity can at last be reconciled if we consider energy-matter and space-time as complementary expressions of information, and she explores how the cosmic hologram underlies the true origin of species and our own evolution. Concurring too with ancient spiritual wisdom, the author offers solid evidence that consciousness is not something we “have” but the fundamental nature of what we and the entire Universe are. With this understanding, we can each transform our own lives and help co-create and in-form the world around us.
Author: Sean A. Hartnoll Publisher: MIT Press ISBN: 0262348020 Category : Science Languages : en Pages : 407
Book Description
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.
Author: Charles Fefferman Publisher: Princeton University Press ISBN: 1400840589 Category : Mathematics Languages : en Pages : 124
Book Description
This book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric in n+2 dimensions that encodes a conformal class of metrics in n dimensions. The ambient metric has an alternate incarnation as the Poincaré metric, a metric in n+1 dimensions having the conformal manifold as its conformal infinity. In this realization, the construction has played a central role in the AdS/CFT correspondence in physics. The existence and uniqueness of the ambient metric at the formal power series level is treated in detail. This includes the derivation of the ambient obstruction tensor and an explicit analysis of the special cases of conformally flat and conformally Einstein spaces. Poincaré metrics are introduced and shown to be equivalent to the ambient formulation. Self-dual Poincaré metrics in four dimensions are considered as a special case, leading to a formal power series proof of LeBrun's collar neighborhood theorem proved originally using twistor methods. Conformal curvature tensors are introduced and their fundamental properties are established. A jet isomorphism theorem is established for conformal geometry, resulting in a representation of the space of jets of conformal structures at a point in terms of conformal curvature tensors. The book concludes with a construction and characterization of scalar conformal invariants in terms of ambient curvature, applying results in parabolic invariant theory.
Author: Mukund Rangamani
Author: Mukund Rangamani
Author: Jie-qiang Wu
Author: Horaƫiu Năstase
Author: Dénes Petz
Author: Albert Einstein
Author: Martin Ammon
Author: Jude Currivan
Author: Sean A. Hartnoll
Author: Charles Fefferman
Author: Jorge Casalderrey-Solana