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.

This book provides an understanding of conformal field theory and its importance to both statistical mechanics and string theory. It introduces the Wess-Zumino-Novokov-Witten (WZNW) models and their current algebras, the affine Kac-Moody algebras.

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.

For almost two decades Prof. Shifman, a clear and pedagogical expositor, has been giving review lectures on frontier topics in theoretical high energy physics. This two-volume book is a collection of some of the best of those lectures. The lectures written in the 1980's and early 1990's have been revised and updated specifically for this publication. The lectures in this book are intended for beginners - graduate students and young researchers - who are about to delve into the intricacies of the theory. They were used by the author in his course ';Advanced Modern Field Theory and Its Applications';, given in the academic year 1994/95 at the University of Minnesota.A wide range of key topics is covered. In Volume 1, the first two chapters are devoted to quantum chromodynamics as the theory of hadrons. The author gives an in-depth discussion of a variety ofpowerful methods based on Wilson's operator product expansion. Chapter 3 (written together with V Novikov, A Vainshtein, and V Zakharov) is the most systematic and pedagogical presentation of instantons in the gauge theories one can find in the literature. Chapter 4 introduces supersymmetry. Chapter 5, concluding this volume, reviews the fascinating dynamics of supersymmetric gauge theories in the strong coupling regime. Chapter 6, which opens Volume 2, is a culmination of the supersymmetric theme. It gives a state-of-the-art description of the breakthrough developments in supersymmetric gauge theories. It has been written specifically for this book by A Vainshtein and the author. Chapter 7 is designed as a primer of two-dimensional conformal field theory, which constitutes the basis of modern string theory. Chapter 8, the last, presents remarkable new findings in quantum mechanics. Every chapter contains exercises and a list of recommended literature.Prof. Shifman has been an active participant and significant contributor in the development of the ideas presented in this book. This accounts for the historical remarks and digressions interspersed in the book, enhancing its pedagogical role. The book will serve as a comprehensive reference and textbook for all graduate students and researchers interested in modern particle physics. It will also be a useful guide for lecturers.

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.

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.

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.