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Epfl Lectures On Conformal Field Theory In D 3 Dimensions
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Book Synopsis EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions by : Slava Rychkov
Download or read book EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions written by Slava Rychkov and published by Springer. This book was released on 2016-09-30 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: This primer develops Conformal Field Theory (CFT) from scratch, whereby CFT is viewed as any conformally-invariant theory that describes a fixed point of a renormalization group flow in quantum field theory. The book is divided into four lectures: Lecture 1 addresses the physical foundations of conformal invariance, while Lecture 2 examines the constraints imposed by conformal symmetry on the correlation functions of local operators, presented using the so-called projective null cone – a procedure also known as the embedding formalism. In turn, Lecture 3 focuses on the radial quantization and the operator product expansion, while Lecture 4 offers a very brief introduction to the conformal bootstrap. Derived from course-based notes, these lectures are intended as a first point of entry to this topic for Master and PhD students alike.
Book Synopsis EPFL Lectures on Conformal Field Theory in D > by : Slava Rychkov
Download or read book EPFL Lectures on Conformal Field Theory in D > written by Slava Rychkov and published by . This book was released on 2017 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis String Field Theory by : Harold Erbin
Download or read book String Field Theory written by Harold Erbin and published by Springer Nature. This book was released on 2021-03-26 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an introduction to string field theory (SFT). String theory is usually formulated in the worldsheet formalism, which describes a single string (first-quantization). While this approach is intuitive and could be pushed far due to the exceptional properties of two-dimensional theories, it becomes cumbersome for some questions or even fails at a more fundamental level. These motivations have led to the development of SFT, a description of string theory using the field theory formalism (second-quantization). As a field theory, SFT provides a rigorous and constructive formulation of string theory. The main focus of the book is the construction of the closed bosonic SFT. The accent is put on providing the reader with the foundations, conceptual understanding and intuition of what SFT is. After reading this book, the reader is able to study the applications from the literature. The book is organized in two parts. The first part reviews the notions of the worldsheet theory that are necessary to build SFT (worldsheet path integral, CFT and BRST quantization). The second part starts by introducing general concepts of SFT from the BRST quantization. Then, it introduces off-shell string amplitudes before providing a Feynman diagrams interpretation from which the building blocks of SFT are extracted. After constructing the closed SFT, the author outlines the proofs of several important properties such as background independence, unitarity and crossing symmetry. Finally, the generalization to the superstring is also discussed.
Book Synopsis Introduction to String Theory by : Sergio Cecotti
Download or read book Introduction to String Theory written by Sergio Cecotti and published by Springer Nature. This book was released on 2023-11-07 with total page 846 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate students typically enter into courses on string theory having little to no familiarity with the mathematical background so crucial to the discipline. As such, this book, based on lecture notes, edited and expanded, from the graduate course taught by the author at SISSA and BIMSA, places particular emphasis on said mathematical background. The target audience for the book includes students of both theoretical physics and mathematics. This explains the book’s "strange" style: on the one hand, it is highly didactic and explicit, with a host of examples for the physicists, but, in addition, there are also almost 100 separate technical boxes, appendices, and starred sections, in which matters discussed in the main text are put into a broader mathematical perspective, while deeper and more rigorous points of view (particularly those from the modern era) are presented. The boxes also serve to further shore up the reader’s understanding of the underlying math. In writing this book, the author’s goal was not to achieve any sort of definitive conciseness, opting instead for clarity and "completeness". To this end, several arguments are presented more than once from different viewpoints and in varying contexts.
Book Synopsis Conformal Field Theory for Particle Physicists by : Marc Gillioz
Download or read book Conformal Field Theory for Particle Physicists written by Marc Gillioz and published by Springer Nature. This book was released on 2023-04-13 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a set of introductory lecture notes on Conformal Field Theory (CFT). Unlike most existing reviews on the subject, CFT is presented here from the perspective of a unitary quantum field theory in Minkowski space-time. The book starts with a non-perturbative formulation of quantum field theory (Wightman axioms) and then, gradually, focuses on the implications of scale and special conformal symmetry, all the way to the modern conformal bootstrap. This approach includes topics such as subtleties of conformal transformations in Minkowski space-time, the construction of Wightman functions and time-ordered correlators both in position- and momentum-space, unitarity bounds derived from the spectral representation, and the appearance of UV and IR divergences. In each chapter, the reader finds useful exercises to master the subject. This book is meant for graduate students in theoretical physics and for more advanced researchers working in high-energy physics who are not necessarily familiar with the concepts of conformal field theory. Prior knowledge of quantum field theory is needed to master the arguments.
Book Synopsis Quantum Gravity and Cosmology Based on Conformal Field Theory by : Ken-ji Hamada
Download or read book Quantum Gravity and Cosmology Based on Conformal Field Theory written by Ken-ji Hamada and published by Cambridge Scholars Publishing. This book was released on 2019-01-18 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is the world beyond the Planck scale that provides the minimum unit of the universe? The goal of quantum gravity is to reveal physical laws in such a world. There, quantum fluctuations of gravity become large, and what is called a background-free world where the concept of time and distance is lost shall be realized. The renormalizable quantum gravity introduced in this book offers a theory in which such a world is described by a certain conformal field theory and a deviation from there is handled as a perturbation. This is the state-of-the-art of modern physics that will help in understanding the history of the universe, from its birth to the present.
Book Synopsis New Frontiers in Fields and Strings by : Joseph Polchinski
Download or read book New Frontiers in Fields and Strings written by Joseph Polchinski and published by World Scientific. This book was released on 2016-11-28 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis AdS3/CFT2 and Holographic Entanglement Entropy by : Jie-qiang Wu
Download or read book AdS3/CFT2 and Holographic Entanglement Entropy written by Jie-qiang Wu and published by Springer Nature. This book was released on 2019-10-18 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Condensed Matter Applications of AdS/CFT by : Andrea Amoretti
Download or read book Condensed Matter Applications of AdS/CFT written by Andrea Amoretti and published by Springer. This book was released on 2017-07-09 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Points, Lines, and Surfaces at Criticality by : Edoardo Lauria
Download or read book Points, Lines, and Surfaces at Criticality written by Edoardo Lauria and published by Springer. This book was released on 2019-07-30 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis offers a fascinating journey through various non-perturbative aspects of Conformal Theories, in particular focusing on the Conformal Bootstrap Programme and its extensions to theories with various degrees of symmetry. Because of the preeminent role of Conformal Theories in Nature, as well as the great generality of the results here obtained, this analysis directly applies to many different areas of research. The content of this thesis is certainly relevant for the physics community as a whole and this relevance is well motivated and discussed along the various chapters of this work. The work is self-contained and starts with an original introduction to conformal theories, defects in such theories and how they lead to constraints on data and an extension of the bootstrap programme. This situation is often realized by critical systems with impurities, topological insulators, or – in the high-energy context – by Wilson and 't Hooft operators. The thesis continues with original research results of the author, including supersymmetric extensions. These results may be relevant non only in the high energy physics context - where supersymmetry is required for the theory to be consistent - but also for condensed matter systems that enjoy supersymmetry emergence at long distances.
Book Synopsis From Classical Mechanics To Quantum Field Theory, A Tutorial by : Manuel Asorey
Download or read book From Classical Mechanics To Quantum Field Theory, A Tutorial written by Manuel Asorey and published by World Scientific. This book was released on 2020-01-14 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects an extended version of the lectures delivered by the authors at the Fall Workshop on Geometry and Physics in the years 2014, 2015, 2016.It aims at introducing advanced graduate and PhD students, as well as young researchers, to current research in mathematics and physics. In particular, it fills the gap between the more physical-oriented and the more mathematical-oriented literature on quantum theory. It introduces various approaches to methods of quantization, along with their impact on modern mathematical methods.
Book Synopsis Space – Time – Matter by : Jochen Brüning
Download or read book Space – Time – Matter written by Jochen Brüning and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-04-09 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph describes some of the most interesting results obtained by the mathematicians and physicists collaborating in the CRC 647 "Space – Time – Matter", in the years 2005 - 2016. The work presented concerns the mathematical and physical foundations of string and quantum field theory as well as cosmology. Important topics are the spaces and metrics modelling the geometry of matter, and the evolution of these geometries. The partial differential equations governing such structures and their singularities, special solutions and stability properties are discussed in detail. Contents Introduction Algebraic K-theory, assembly maps, controlled algebra, and trace methods Lorentzian manifolds with special holonomy – Constructions and global properties Contributions to the spectral geometry of locally homogeneous spaces On conformally covariant differential operators and spectral theory of the holographic Laplacian Moduli and deformations Vector bundles in algebraic geometry and mathematical physics Dyson–Schwinger equations: Fix-point equations for quantum fields Hidden structure in the form factors ofN = 4 SYM On regulating the AdS superstring Constraints on CFT observables from the bootstrap program Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities Yangian symmetry in maximally supersymmetric Yang-Mills theory Wave and Dirac equations on manifolds Geometric analysis on singular spaces Singularities and long-time behavior in nonlinear evolution equations and general relativity
Book Synopsis Fermions and Anomalies in Quantum Field Theories by : Loriano Bonora
Download or read book Fermions and Anomalies in Quantum Field Theories written by Loriano Bonora and published by Springer Nature. This book was released on 2023-05-04 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a modern view of anomalies in quantum field theories. It is divided into six parts. The first part is preparatory covering an introduction to fermions, a description of the classical symmetries, and a short introduction to conformal symmetry. The second part of the book is devoted to the relation between anomalies and cohomology. The third part deals with perturbative methods to compute gauge, diffeomorphism and trace anomalies. In the fourth part the same anomalies are calculated with non-perturbative heat-kernel-like methods. Part five is devoted to the family's index theorem and its application to chiral anomalies, and to the differential characters and their applications to global anomalies. Part six is devoted to special topics including a complete calculation of trace and diffeomorphism anomalies of a Dirac fermion in a MAT background in two dimensions, Wess-Zumino terms in field theories, sigma models, their local and global anomalies and their cancelation, and finally the analysis of the worldsheet, sigma model, and target space anomalies of string and superstring theories. The book is targeted to researchers and graduate students.
Book Synopsis Lectures on the Random Field Ising Model by : Slava Rychkov
Download or read book Lectures on the Random Field Ising Model written by Slava Rychkov and published by Springer Nature. This book was released on 2023-10-09 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the Random Field Ising Model (RFIM) – a paradigmatic spin model featuring a frozen disordering field. The focus is on the second-order phase transition between the paramagnetic and ferromagnetic phases, and the associated critical exponents. The book starts by summarizing the current knowledge about the RFIM from experiments, numerical simulations and rigorous mathematical results. It then reviews the classic theoretical works from the 1970’s which suggested a property of dimensional reduction – that the RFIM critical exponents should be the same as for the ordinary, non-disordered, Ising model of lower dimensionality, and related this an emergent Parisi-Sourlas supersymmetry. As is now known, these remarkable properties only hold when the spatial dimensionality of the model is larger than a critical dimension. The book presents a method to estimate the critical dimension, using standard tools such as the replica trick and perturbative renormalization group, whose result is in agreement with the numerical simulations. Some more elementary steps in the derivations are left as exercises for the readers. This book is of interest to researchers, PhD students and advanced master students specializing in statistical field theory.
Book Synopsis Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1 by : Vladimir Dobrev
Download or read book Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1 written by Vladimir Dobrev and published by Springer. This book was released on 2018-11-28 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first volume of proceedings from the joint conference X International Symposium “Quantum Theory and Symmetries” (QTS-X) and XII International Workshop “Lie Theory and Its Applications in Physics” (LT-XII), held on 19–25 June 2017 in Varna, Bulgaria. The QTS series was founded on the core principle that symmetries underlie all descriptions of quantum systems. It has since evolved into a symposium at the forefront of theoretical and mathematical physics. The LT series covers the whole field of Lie theory in its widest sense, together with its applications in many areas of physics. As an interface between mathematics and physics, the workshop serves as a meeting place for mathematicians and theoretical and mathematical physicists. In dividing the material between the two volumes, the Editor has sought to select papers that are more oriented toward mathematics for the first volume, and those focusing more on physics for the second. However, this division is relative, since many papers are equally suitable for either volume. The topics addressed in this volume represent the latest trends in the fields covered by the joint conferences: representation theory, integrability, entanglement, quantum groups, number theory, conformal geometry, quantum affine superalgebras, noncommutative geometry. Further, they present various mathematical results: on minuscule modules, symmetry breaking operators, Kashiwara crystals, meta-conformal invariance, the superintegrable Zernike system.
Book Synopsis A Mathematical Introduction to Conformal Field Theory by : Martin Schottenloher
Download or read book A Mathematical Introduction to Conformal Field Theory written by Martin Schottenloher and published by Springer Science & Business Media. This book was released on 2008-09-15 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part I gives a detailed, self-contained and mathematically rigorous exposition of classical conformal symmetry in n dimensions and its quantization in two dimensions. The conformal groups are determined and the appearence of the Virasoro algebra in the context of the quantization of two-dimensional conformal symmetry is explained via the classification of central extensions of Lie algebras and groups. Part II surveys more advanced topics of conformal field theory such as the representation theory of the Virasoro algebra, conformal symmetry within string theory, an axiomatic approach to Euclidean conformally covariant quantum field theory and a mathematical interpretation of the Verlinde formula in the context of moduli spaces of holomorphic vector bundles on a Riemann surface.
Book Synopsis Conformal Field Theory by : Sergei V Ketov
Download or read book Conformal Field Theory written by Sergei V Ketov and published by World Scientific. This book was released on 1995-02-28 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conformal field theory is an elegant and powerful theory in the field of high energy physics and statistics. In fact, it can be said to be one of the greatest achievements in the development of this field. Presented in two dimensions, this book is designed for students who already have a basic knowledge of quantum mechanics, field theory and general relativity. The main idea used throughout the book is that conformal symmetry causes both classical and quantum integrability. Instead of concentrating on the numerous applications of the theory, the author puts forward a discussion of the general methods of conformal field theory as a physical theory. Hence the book provides in a self-contained way the necessary knowledge and “conformal” intuition which underline the various applications of conformal field theory. It is aimed to assist students and professionals in the study of the theory from its first principles and in applying the methods in their own research. The first of its kind, this book promises to give a detailed and comprehensive insight into the workings of conformal field theory.
