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.

The goal of this text is to introduce, in a very elementary way, the concept of anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence to condensed matter physicists. This theory relates a gravity theory in a (d+1)-dimensional anti-de Sitter space

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

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.

Since its discovery in 1997 by Maldacena, AdS/CFT correspondence has become one of the prime subjects of interest in string theory, as well as one of the main meeting points between theoretical physics and mathematics. On the physical side, it provides a duality between a theory of quantum gravity and a field theory. The mathematical counterpart is the relation between Einstein metrics and their conformal boundaries. The correspondence has been intensively studied, and a lot of progress emerged from the confrontation of viewpoints between mathematics and physics. Written by leading experts and directed at research mathematicians and theoretical physicists as well as graduate students, this volume gives an overview of this important area both in theoretical physics and in mathematics. It contains survey articles giving a broad overview of the subject and of the main questions, as well as more specialized articles providing new insight both on the Riemannian side and on the Lorentzian side of the theory.

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.

The book deals with applications of the AdS/CFT correspondence to strongly coupled condensed matter systems. In particular, it concerns with the study of thermo-electric transport properties of holographic models exhibiting momentum dissipation and their possible applications to the transport properties of strange metals. The present volume constitutes one of the few examples in the literature in which the topic is carefully reviewed both from the experimental and theoretical point of view, including not only holographic results but also standard condensed matter achievements developed in the past decades. This work might be extremely useful both for scientific and pedagogical purposes.

The discovery of a duality between Anti-de Sitter spaces (AdS) and Conformal Field Theories (CFT) has led to major advances in our understanding of quantum field theory and quantum gravity. String theory methods and AdS/CFT correspondence maps provide new ways to think about difficult condensed matter problems. String theory methods based on the AdS/CFT correspondence allow us to transform problems so they have weak interactions and can be solved more easily. They can also help map problems to different descriptions, for instance mapping the description of a fluid using the Navier–Stokes equations to the description of an event horizon of a black hole using Einstein's equations. This textbook covers the applications of string theory methods and the mathematics of AdS/CFT to areas of condensed matter physics. Bridging the gap between string theory and condensed matter, this is a valuable textbook for students and researchers in both fields.

This volume is a compilation of lectures delivered at the TASI 2015 summer school, 'New Frontiers in Fields and Strings', held at the University of Colorado Boulder in June 2015. The school focused on topics in theoretical physics of interest to contemporary researchers in quantum field theory and string theory. The lectures are accessible to graduate students in the initial stages of their research careers.

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.