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| conformal field theory francesco: Conformal Field Theory Philippe Francesco, Pierre Mathieu, David Senechal, 2012-12-06 Filling an important gap in the literature, this comprehensive text develops conformal field theory from first principles. The treatment is self-contained, pedagogical, and exhaustive, and includes a great deal of background material on quantum field theory, statistical mechanics, Lie algebras and affine Lie algebras. The many exercises, with a wide spectrum of difficulty and subjects, complement and in many cases extend the text. The text is thus not only an excellent tool for classroom teaching but also for individual study. Intended primarily for graduate students and researchers in theoretical high-energy physics, mathematical physics, condensed matter theory, statistical physics, the book will also be of interest in other areas of theoretical physics and mathematics. It will prepare the reader for original research in this very active field of theoretical and mathematical physics. |
| conformal field theory francesco: Conformal Field Theory Philippe Francesco, Pierre Mathieu, David Sénéchal, 1997 Filling an important gap in the literature, this comprehensive text develops conformal field theory from first principles. The treatment is self-contained, pedagogical, and exhaustive, and includes a great deal of background material on quantum field theory, statistical mechanics, Lie algebras and affine Lie algebras. The many exercises, with a wide spectrum of difficulty and subjects, complement and in many cases extend the text. The text is thus not only an excellent tool for classroom teaching but also for individual study. Intended primarily for graduate students and researchers in theoretical high-energy physics, mathematical physics, condensed matter theory, statistical physics, the book will also be of interest in other areas of theoretical physics and mathematics. It will prepare the reader for original research in this very active field of theoretical and mathematical physics. |
| conformal field theory francesco: Conformal Field Theory Philippe Francesco, Pierre Mathieu, David Senechal, 1996-12-13 |
| conformal field theory francesco: Introduction to Conformal Field Theory Ralph Blumenhagen, Erik Plauschinn, 2009-07-11 Based on class-tested notes, this text offers an introduction to Conformal Field Theory with a special emphasis on computational techniques of relevance for String Theory. It introduces Conformal Field Theory at a basic level, Kac-Moody algebras, one-loop partition functions, Superconformal Field Theories, Gepner Models and Boundary Conformal Field Theory. Eventually, the concept of orientifold constructions is explained in detail for the example of the bosonic string. In providing many detailed CFT calculations, this book is ideal for students and scientists intending to become acquainted with CFT techniques relevant for string theory but also for students and non-specialists from related fields. |
| conformal field theory francesco: A Mathematical Introduction to Conformal Field Theory Martin Schottenloher, 2008-09-15 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. |
| conformal field theory francesco: Conformal Field Theory Sergei V Ketov, 1995-02-28 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. |
| conformal field theory francesco: Conformal Field Theory Philippe Francesco, Pierre Mathieu, David Senechal, 2011-09-17 Filling an important gap in the literature, this comprehensive text develops conformal field theory from first principles. The treatment is self-contained, pedagogical, and exhaustive, and includes a great deal of background material on quantum field theory, statistical mechanics, Lie algebras and affine Lie algebras. The many exercises, with a wide spectrum of difficulty and subjects, complement and in many cases extend the text. The text is thus not only an excellent tool for classroom teaching but also for individual study. Intended primarily for graduate students and researchers in theoretical high-energy physics, mathematical physics, condensed matter theory, statistical physics, the book will also be of interest in other areas of theoretical physics and mathematics. It will prepare the reader for original research in this very active field of theoretical and mathematical physics. |
| conformal field theory francesco: Conformal Field Theory and Critical Phenomena in Two Dimensional Systems A.B. Zamolodchikov, 1989-01-31 |
| conformal field theory francesco: Strings, Conformal Fields, and Topology Michio Kaku, 2012-12-06 Following on the foundations laid in his earlier book Introduction to Superstrings, Professor Kaku discusses such topics as the classification of conformal string theories, the non-polynomial closed string field theory, matrix models, and topological field theory. The presentation of the material is self-contained, and several chapters review material expounded in the earlier book. This book provides students with an understanding of the main areas of current progress in string theory, placing the reader at the forefront of current research. |
| conformal field theory francesco: Vertex Operator Algebras and the Monster Igor Frenkel, James Lepowsky, Arne Meurman, 1989-04-11 This work is motivated by and develops connections between several branches of mathematics and physics--the theories of Lie algebras, finite groups and modular functions in mathematics, and string theory in physics. The first part of the book presents a new mathematical theory of vertex operator algebras, the algebraic counterpart of two-dimensional holomorphic conformal quantum field theory. The remaining part constructs the Monster finite simple group as the automorphism group of a very special vertex operator algebra, called the moonshine module because of its relevance to monstrous moonshine. |
| conformal field theory francesco: EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions Slava Rychkov, 2016-09-30 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. |
| conformal field theory francesco: Introduction to AdS/CFT Correspondence Horaƫiu Năstase, 2015-09-10 A pedagogical and self-contained introduction to AdS/CFT correspondence aimed at graduate students and researchers across theoretical physics. |
| conformal field theory francesco: Quantum Field Theory: A Tourist Guide for Mathematicians Gerald B. Folland, 2021-02-03 Quantum field theory has been a great success for physics, but it is difficult for mathematicians to learn because it is mathematically incomplete. Folland, who is a mathematician, has spent considerable time digesting the physical theory and sorting out the mathematical issues in it. Fortunately for mathematicians, Folland is a gifted expositor. The purpose of this book is to present the elements of quantum field theory, with the goal of understanding the behavior of elementary particles rather than building formal mathematical structures, in a form that will be comprehensible to mathematicians. Rigorous definitions and arguments are presented as far as they are available, but the text proceeds on a more informal level when necessary, with due care in identifying the difficulties. The book begins with a review of classical physics and quantum mechanics, then proceeds through the construction of free quantum fields to the perturbation-theoretic development of interacting field theory and renormalization theory, with emphasis on quantum electrodynamics. The final two chapters present the functional integral approach and the elements of gauge field theory, including the Salam–Weinberg model of electromagnetic and weak interactions. |
| conformal field theory francesco: Vertex Algebras for Beginners Victor G. Kac, 1998 This is an improved and expanded edition of Kac's original introduction to algebraic aspects of conformal field theory which was published by the AMS in 1996. This revised edition is based on courses given by the author at MIT and at Rome University in Spring 1997. |
| conformal field theory francesco: New Frontiers In Fields And Strings (Tasi 2015) - Proceedings Of The 2015 Theoretical Advanced Study Institute In Elementary Particle Physics Joseph Polchinski, Pedro Vieira, Oliver Dewolfe, 2016-11-28 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. |
| conformal field theory francesco: Introduction to Strings and Branes Peter West, 2012-07-05 Supersymmetry, strings and branes are believed to be the essential ingredients in a single unified consistent theory of physics. This book gives a detailed, step-by-step introduction to the theoretical foundations required for research in strings and branes. After a study of the different formulations of the bosonic and supersymmetric point particles, the classical and quantum bosonic and supersymmetric string theories are presented. This book includes accounts of brane dynamics and D-branes and the T, S and U duality symmetries of string theory. The historical derivation of string theory is given as well as the sum over the world-sheet approach to the interacting string. More advanced topics include string field theory and Kac–Moody symmetries. The book contains pedagogical accounts of conformal quantum field theory, supergravity theories, Clifford algebras and spinors, and Lie algebras. It is essential reading for graduate students and researchers wanting to learn strings and branes. |
| conformal field theory francesco: Strings, Conformal Fields, and M-Theory Michio Kaku, 2012-12-06 String theory continues to progress at an astonishing rate, and this book brings the reader up to date with the latest developments and the most active areas of research in the field. Building on the foundations laid in his Introduction to Superstrings and M Theory, Professor Kaku discusses such topics as the classification of conformal string theories, knot theory, the Yang-Baxter relation, quantum groups, and the insights into 11-dimensional strings recently obtained from M-theory. New chapters discuss such topics as Seiberg- Witten theory, M theory and duality., and D-branes. Several chapters review the fundamentals of string theory, making the presentation of the material self-contained while keeping overlap with the earlier book to a minimum. This book conveys the vitality of the current research and places readers at its forefront. |
| conformal field theory francesco: Quantum Field Theory and Condensed Matter Ramamurti Shankar, 2017-08-30 Providing a broad review of many techniques and their application to condensed matter systems, this book begins with a review of thermodynamics and statistical mechanics, before moving onto real and imaginary time path integrals and the link between Euclidean quantum mechanics and statistical mechanics. A detailed study of the Ising, gauge-Ising and XY models is included. The renormalization group is developed and applied to critical phenomena, Fermi liquid theory and the renormalization of field theories. Next, the book explores bosonization and its applications to one-dimensional fermionic systems and the correlation functions of homogeneous and random-bond Ising models. It concludes with Bohm-Pines and Chern-Simons theories applied to the quantum Hall effect. Introducing the reader to a variety of techniques, it opens up vast areas of condensed matter theory for both graduate students and researchers in theoretical, statistical and condensed matter physics. |
| conformal field theory francesco: Strings, Branes and Extra Dimensions Steven Scott Gubser, J. D. Lykken, 2004 This book covers some recent advances in string theory and extra dimensions. Intended mainly for advanced graduate students in theoretical physics, it presents a rare combination of formal and phenomenological topics, based on the annual lectures given at the School of the Theoretical Advanced Study Institute (2001) OCo a traditional event that brings together graduate students in high energy physics for an intensive course of advanced learning. The lecturers in the School are leaders in their fields. The first lecture, by E DOCOHoker and D Freedman, is a systematic introduction to the gaugeOCogravity correspondence, focusing in particular on correlation functions in the conformal case. The second, by L Dolan, provides an introduction to perturbative string theory, including recent advances on backgrounds involving Ramond-Ramond fluxes. The third, by S Gubser, explains some of the basic facts about special holonomy and its uses in string theory and M-theory. The fourth, by J Hewett, surveys the TeV phenomenology of theories with large extra dimensions. The fifth, by G Kane, presents the case for supersymmetry at the weak scale and some of its likely experimental consequences. The sixth, by A Liddle, surveys recent developments in cosmology, particularly with regard to recent measurements of the CMB and constraints on inflation. The seventh, by B Ovrut, presents the basic features of heterotic M-theory, including constructions that contain the Standard Model. The eighth, by K Rajagopal, explains the recent advances in understanding QCD at low temperatures and high densities in terms of color superconductivity. The ninth, by M Sher, summarizes grand unified theories and baryogenesis, including discussions of supersymmetry breaking and the Standard Model Higgs mechanism. The tenth, by M Spiropulu, describes collider physics, from a survey of current and future machines to examples of data analyses relevant to theories beyond the Standard Model. The eleventh, by M Strassler, is an introduction to supersymmetric gauge theory, focusing on Wilsonian renormalization and analogies between three- and four-dimensional theories. The twelfth, by W Taylor and B Zwiebach, introduces string field theory and discusses recent advances in understanding open string tachyon condensation. The thirteenth, by D Waldram, discusses explicit model building in heterotic M-theory, emphasizing the role of the E8 gauge fields. The written presentation of these lectures is detailed yet straightforward, and they will be of use to both students and experienced researchers in high-energy theoretical physics for years to come. The proceedings have been selected for coverage in: . OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings). OCo CC Proceedings OCo Engineering & Physical Sciences. |
| conformal field theory francesco: Conformal Invariance And Applications To Statistical Mechanics C Itzykson, H Saleur, Jean-bernard Zuber, 1998-09-29 This volume contains Introductory Notes and major reprints on conformal field theory and its applications to 2-dimensional statistical mechanics of critical phenomena. The subject relates to many different areas in contemporary physics and mathematics, including string theory, integrable systems, representations of infinite Lie algebras and automorphic functions. |
| conformal field theory francesco: Vertex Algebras and Algebraic Curves Edward Frenkel, David Ben-Zvi, 2004-08-25 Vertex algebras are algebraic objects that encapsulate the concept of operator product expansion from two-dimensional conformal field theory. Vertex algebras are fast becoming ubiquitous in many areas of modern mathematics, with applications to representation theory, algebraic geometry, the theory of finite groups, modular functions, topology, integrable systems, and combinatorics. This book is an introduction to the theory of vertex algebras with a particular emphasis on the relationship with the geometry of algebraic curves. The notion of a vertex algebra is introduced in a coordinate-independent way, so that vertex operators become well defined on arbitrary smooth algebraic curves, possibly equipped with additional data, such as a vector bundle. Vertex algebras then appear as the algebraic objects encoding the geometric structure of various moduli spaces associated with algebraic curves. Therefore they may be used to give a geometric interpretation of various questions of representation theory. The book contains many original results, introduces important new concepts, and brings new insights into the theory of vertex algebras. The authors have made a great effort to make the book self-contained and accessible to readers of all backgrounds. Reviewers of the first edition anticipated that it would have a long-lasting influence on this exciting field of mathematics and would be very useful for graduate students and researchers interested in the subject. This second edition, substantially improved and expanded, includes several new topics, in particular an introduction to the Beilinson-Drinfeld theory of factorization algebras and the geometric Langlands correspondence. |
| conformal field theory francesco: String Field Theory Harold Erbin, 2021-03-26 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. |
| conformal field theory francesco: Gauge Fields and Strings Polyakov, 2018-05-02 Based on his own work, the author synthesizes the most promising approaches and ideals in field theory today. He presents such subjects as statistical mechanics, quantum field theory and their interrelation, continuous global symmetry, non-Abelian gauge fields, instantons and the quantam theory of loops, and quantum strings and random surfaces. This book is aimed at postgraduate students studying field theory and statistical mechanics, and for research workers in continuous global theory. |
| conformal field theory francesco: Boundary Conformal Field Theory and the Worldsheet Approach to D-Branes Andreas Recknagel, Volker Schomerus, 2013-11-28 Boundary conformal field theory is concerned with a class of two-dimensional quantum field theories which display a rich mathematical structure and have many applications ranging from string theory to condensed matter physics. In particular, the framework allows discussion of strings and branes directly at the quantum level. Written by internationally renowned experts, this comprehensive introduction to boundary conformal field theory reaches from theoretical foundations to recent developments, with an emphasis on the algebraic treatment of string backgrounds. Topics covered include basic concepts in conformal field theory with and without boundaries, the mathematical description of strings and D-branes, and the geometry of strongly curved spacetime. The book offers insights into string geometry that go beyond classical notions. Describing the theory from basic concepts, and providing numerous worked examples from conformal field theory and string theory, this reference is of interest to graduate students and researchers in physics and mathematics. |
| conformal field theory francesco: Sixteenth International Congress on Mathematical Physics Pavel Exner, 2010 The International Congress on Mathematical Physics is the flagship conference in this exciting field. Convening every three years, it gives a survey on the progress achieved in all branches of mathematical physics. It also provides a superb platform to discuss challenges and new ideas. The present volume collects material from the XVIth ICMP which was held in Prague, August 2009, and features most of the plenary lectures and invited lectures in topical sessions as well as information on other parts of the congress program. This volume provides a broad coverage of the field of mathematical physics, from dominantly mathematical subjects to particle physics, condensed matter, and application of mathematical physics methods in various areas such as astrophysics and ecology, amongst others. |
| conformal field theory francesco: Holographic Quantum Matter Sean A. Hartnoll, Andrew Lucas, Subir Sachdev, 2018-03-16 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. |
| conformal field theory francesco: Quantization of Gauge Systems Marc Henneaux, Claudio Teitelboim, 1992 This book is a systematic study of the classical and quantum theories of gauge systems. It starts with Dirac's analysis showing that gauge theories are constrained Hamiltonian systems. The classical foundations of BRST theory are then laid out with a review of the necessary concepts from homological algebra. Reducible gauge systems are discussed, and the relationship between BRST cohomology and gauge invariance is carefully explained. The authors then proceed to the canonical quantization of gauge systems, first without ghosts (reduced phase space quantization, Dirac method) and second in the BRST context (quantum BRST cohomology). The path integral is discussed next. The analysis covers indefinite metric systems, operator insertions, and Ward identities. The antifield formalism is also studied and its equivalence with canonical methods is derived. The examples of electromagnetism and abelian 2-form gauge fields are treated in detail. The book gives a general and unified treatment of the subject in a self-contained manner. Exercises are provided at the end of each chapter, and pedagogical examples are covered in the text. |
| conformal field theory francesco: Quantum Field Theory and Critical Phenomena Jean Zinn-Justin, 1993 Describes particle physics and critical phenomena in statistical mechanics in a unified framework, incorporating graduate lecture notes from the 1970s and 1980s at several universities in Europe and the US. Deals with general field theory, functional integrals, and functional methods; renormalization properties of theories with symmetries and specific applications to particle physics; lattice gauge theories and asymptotic freedom in four dimensions; and the role of instantons and the application of instanton calculus to the large-order behavior of perturbation theory and the problem of summation of the perturbative expansion. Several chapters close with exercise, solutions or hints for which are provided. No dates are noted for the previous editions. Annotation copyright by Book News, Inc., Portland, OR |
| conformal field theory francesco: Quantum Field Theory Bertfried Fauser, Jürgen Tolksdorf, Eberhard Zeidler, 2009-06-02 The present volume emerged from the 3rd `Blaubeuren Workshop: Recent Developments in Quantum Field Theory', held in July 2007 at the Max Planck Institute of Mathematics in the Sciences in Leipzig/Germany. All of the contributions are committed to the idea of this workshop series: To bring together outstanding experts working in the field of mathematics and physics to discuss in an open atmosphere the fundamental questions at the frontier of theoretical physics. |
| conformal field theory francesco: W-symmetry P. Bouwknegt, K. Schoutens, 1995 W-symmetry is an extension of conformal symmetry in two dimensions. Since its introduction in 1985, W-symmetry has become one of the central notions in the study of two-dimensional conformal field theory. The mathematical structures that underlie W-symmetry are so-called W-algebras, which are higher-spin extensions of the Virasoro algebra. This book contains a collection of papers on W-symmetry, covering the period from 1985 through 1993. Its main focus is the construction of W-algebras and their representation theory. A recurrent theme is the intimate connection between W-algebras and affine Lie algebras. Some of the applications, in particular W-gravity, are also covered.The significance of this reprint volume is that there are no textbooks entirely devoted to the subject. |
| conformal field theory francesco: Supersymmetry and Supergravity Julius Wess, Jonathan Bagger, 1992-03-23 This widely acclaimed introduction to N = 1 supersymmetry and supergravity is aimed at readers familiar with relativistic quantum field theory who wish to learn about the supersymmetry algebra. In this new volume Supersymmetry and Supergravity has been greatly expanded to include a detailed derivation of the most general coupling of super-symmetric gauge theory to supergravity. The final result is the starting point for phenomenological studies of supersymmetric theories. The book is distinguished by its pedagogical approach to supersymmetry. It develops several topics in advanced field theory as the need arises. It emphasizes the logical coherence of the subject and should appeal to physicists whose interests range from the mathematical to the phenomenological. In praise of the first edition: A beautiful exposition of the original ideas of Wess and Zumino in formulating N = 1 supersymmetry and supergravity theories, couched in the language of superfields introduced by Strathdee and the reviewer.... [All] serious students of particle physics would do well to acquire a copy.--Abdus Salam, Nature An excellent introduction to this exciting area of theoretical physics.--C. J. Isham, Physics Bulletin |
| conformal field theory francesco: Gauge/Gravity Duality Martin Ammon, Johanna Erdmenger, 2015-04-09 Gauge/gravity duality creates new links between quantum theory and gravity. It has led to new concepts in mathematics and physics, and provides new tools to solve problems in many areas of theoretical physics. This book is the first textbook on this important topic, enabling graduate students and researchers in string theory and particle, nuclear and condensed matter physics to get acquainted with the subject. Focusing on the fundamental aspects as well as on the applications, this textbook guides readers through a thorough explanation of the central concepts of gauge/gravity duality. For the AdS/CFT correspondence, it explains in detail how string theory provides the conjectured map. Generalisations to less symmetric cases of gauge/gravity duality and their applications are then presented, in particular to finite temperature and density, hydrodynamics, QCD-like theories, the quark-gluon plasma and condensed matter systems. The textbook features a large number of exercises, with solutions available online at www.cambridge.org/9781107010345. |
| conformal field theory francesco: Non-Perturbative Field Theory Yitzhak Frishman, Jacob Sonnenschein, 2023-07-27 Providing a new perspective on quantum field theory, this book gives a pedagogical exposition of non-perturbative methods in relativistic quantum field theory and introduces the reader to modern research in theoretical physics. After describing non-perturbative methods in detail, it uses these methods to explore two-dimensional and four-dimensional gauge dynamics. The book concludes with a summary emphasizing the interplay between two- and four-dimensional gauge theories. Aimed at graduate students and researchers, this book covers topics from two-dimensional conformal symmetry, affine Lie algebras, solitons, integrable models, bosonization, and 't Hooft model, to four-dimensional conformal invariance, integrability, large N expansion, Skyrme model, monopoles and instantons. Applications, first to simple field theories and gauge dynamics in two dimensions, and then to gauge theories in four dimensions and quantum chromodynamics in particular, are thoroughly described. Published originally in 2010, this title has been reissued as an Open Access publication on Cambridge Core. |
| conformal field theory francesco: Scaling and Renormalization in Statistical Physics John Cardy, 1996-04-26 This text provides a thoroughly modern graduate-level introduction to the theory of critical behaviour. It begins with a brief review of phase transitions in simple systems, then goes on to introduce the core ideas of the renormalisation group. |
| conformal field theory francesco: A First Course in String Theory Barton Zwiebach, 2009-01-22 String theory made understandable. Barton Zwiebach is once again faithful to his goal of making string theory accessible to undergraduates. He presents the main concepts of string theory in a concrete and physical way to develop intuition before formalism, often through simplified and illustrative examples. Complete and thorough in its coverage, this new edition now includes AdS/CFT correspondence and introduces superstrings. It is perfectly suited to introductory courses in string theory for students with a background in mathematics and physics. New sections cover strings on orbifolds, cosmic strings, moduli stabilization, and the string theory landscape. Now with almost 300 problems and exercises, with password-protected solutions for instructors at www.cambridge.org/zwiebach. |
| conformal field theory francesco: Conformal Field Theory for Particle Physicists Marc Gillioz, 2023-04-13 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. |
| conformal field theory francesco: An Operator Identity Glen E. Baxter, 1957 Let M be a matrix, Let M+ be formed by setting equal to zero all elements of M on or below the diagonal, and Let M- = M - M+. Equations P = I + s(MP)+ and Q = I + s(QM)- are investigated and their solutions applied to certain problems in the theory of probability where M is the transition probability matrix of a Markov chain. Extension to certain operators M is carried through. |
| conformal field theory francesco: Fields, Strings and Critical Phenomena E. Brézin, Jean Zinn-Justin, 1990 Hardbound. This session of the Summer School in Theoretical Physics concentrated on the recent advances in areas of physics ranging from (super)strings to field theory and statistical mechanics. The articles contained in this volume provide a stimulating and up-to-date account of a rapidly growing subject.Discussion focussed on the many points of convergence between field theory and statistical mechanics: conformal field theory, field theory on a lattice, the study of strongly correlated electron systems, as in the Hubbard model, leading to topological Lagrangians, which are perhaps the key of the understanding of high Tc superconductivity or the fractional quantum Hall effect. The critical phenomena in (1+1) dimensions, in the domain in which quantum fluctuations are strong, are described for antiferromagnetic couplings by relativistic theories in which the methods of abelian or non-abelian bosonization are particularly powerful. |
| conformal field theory francesco: A Primer on String Theory Volker Schomerus, 2017-07-06 A concise introduction to string theory explaining central concepts, mathematical tools and recent developments in the field of physics. Covering fundamental concepts including how strings interact with each other, this book is perfect for students with no prior knowledge as well as scholars from other disciplines. |
| conformal field theory francesco: Lectures on Quantum Gravity Andres Gomberoff, Donald Marolf, 2006-05-30 The 2002 Pan-American Advanced Studies Institute School on Quantum Gravity was held at the Centro de Estudios Cientificos (CECS),Valdivia, Chile, January 4-14, 2002. The school featured lectures by ten speakers, and was attended by nearly 70 students from over 14 countries. A primary goal was to foster interaction and communication between participants from different cultures, both in the layman’s sense of the term and in terms of approaches to quantum gravity. We hope that the links formed by students and the school will persist throughout their professional lives, continuing to promote interaction and the essential exchange of ideas that drives research forward. This volume contains improved and updated versions of the lectures given at the School. It has been prepared both as a reminder for the participants, and so that these pedagogical introductions can be made available to others who were unable to attend. We expect them to serve students of all ages well. |
Conformal map - Wikipedia
Conformal maps preserve both angles and the shapes of infinitesimally small figures, but not necessarily their size or curvature. The conformal property may be described in terms of the …
CONFORMAL Definition & Meaning - Merriam-Webster
The meaning of CONFORMAL is leaving the size of the angle between corresponding curves unchanged. How to use conformal in a sentence.
Conformal Mapping -- from Wolfram MathWorld
May 22, 2025 · A conformal mapping, also called a conformal map, conformal transformation, angle-preserving transformation, or biholomorphic map, is a transformation w=f (z) that …
CONFORMAL definition and meaning | Collins English Dictionary
2 meanings: 1. mathematics a. (of a transformation) preserving the angles of the depicted surface b. (of a parameter) relating.... Click for more definitions.
CONFORMAL Definition & Meaning | Dictionary.com
Relating to the mapping of a surface or region onto another surface so that all angles between intersecting curves remain unchanged. Relating to a map projection in which small areas are …
Conformal - definition of conformal by The Free Dictionary
Define conformal. conformal synonyms, conformal pronunciation, conformal translation, English dictionary definition of conformal. adj. 1. Mathematics Designating or specifying a mapping of a …
11.1: Geometric Definition of Conformal Mappings
Conformal maps are functions on C C that preserve the angles between curves. More precisely: Suppose f(z) f (z) is differentiable at z0 z 0 and γ(t) γ (t) is a smooth curve through z0 z 0.
conformal, adj. meanings, etymology and more | Oxford English …
What does the adjective conformal mean? There are two meanings listed in OED's entry for the adjective conformal. See ‘Meaning & use’ for definitions, usage, and quotation evidence. …
conformal - Wiktionary, the free dictionary
Jan 2, 2025 · conformal (comparative more conformal, superlative most conformal) That conforms, especially to the shape of something.
What does conformal mean? - Definitions.net
Definition of conformal in the Definitions.net dictionary. Meaning of conformal. What does conformal mean? Information and translations of conformal in the most comprehensive …
Conformal map - Wikipedia
Conformal maps preserve both angles and the shapes of infinitesimally small figures, but not necessarily their size or curvature. The conformal property may be described in terms of the …
CONFORMAL Definition & Meaning - Merriam-Webster
The meaning of CONFORMAL is leaving the size of the angle between corresponding curves unchanged. How to use conformal in a sentence.
Conformal Mapping -- from Wolfram MathWorld
May 22, 2025 · A conformal mapping, also called a conformal map, conformal transformation, angle-preserving transformation, or biholomorphic map, is a transformation w=f (z) that …
CONFORMAL definition and meaning | Collins English Dictionary
2 meanings: 1. mathematics a. (of a transformation) preserving the angles of the depicted surface b. (of a parameter) relating.... Click for more definitions.
CONFORMAL Definition & Meaning | Dictionary.com
Relating to the mapping of a surface or region onto another surface so that all angles between intersecting curves remain unchanged. Relating to a map projection in which small areas are …
Conformal - definition of conformal by The Free Dictionary
Define conformal. conformal synonyms, conformal pronunciation, conformal translation, English dictionary definition of conformal. adj. 1. Mathematics Designating or specifying a mapping of a …
11.1: Geometric Definition of Conformal Mappings
Conformal maps are functions on C C that preserve the angles between curves. More precisely: Suppose f(z) f (z) is differentiable at z0 z 0 and γ(t) γ (t) is a smooth curve through z0 z 0.
conformal, adj. meanings, etymology and more | Oxford English …
What does the adjective conformal mean? There are two meanings listed in OED's entry for the adjective conformal. See ‘Meaning & use’ for definitions, usage, and quotation evidence. …
conformal - Wiktionary, the free dictionary
Jan 2, 2025 · conformal (comparative more conformal, superlative most conformal) That conforms, especially to the shape of something.
What does conformal mean? - Definitions.net
Definition of conformal in the Definitions.net dictionary. Meaning of conformal. What does conformal mean? Information and translations of conformal in the most comprehensive …
