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Fortschritte der Physik/Progress of Physics

Introduction to Conformal Field Theory

A.N. Schellekens

Published Jan 1, 1996• 35 citations
Publisher

Abstract

An elementary introduction to conformal field theory is given. Topics include free bosons and fermions, orbifolds, affine Lie algebras, coset conformal field theories, superconformal theories, correlation functions on the sphere, partition functions and modular invariance.
DOI
10.1002/prop.2190440802

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This 1996 book is an introduction to integrability and conformal field theory in two dimensions using quantum groups. The book begins with a brief introduction to S-matrices, spin chains and vertex models as a prelude to the study of Yang–Baxter algebras and the Bethe ansatz. The basic ideas of integrable systems are then introduced, giving particular emphasis to vertex and face models. Special attention is given to explaining the underlying mathematical tools, including braid groups, knot invariants and towers of algebra. The book then goes on to give a detailed introduction to quantum groups as a prelude to chapters on integrable models, two-dimensional conformal field theories and superconformal field theories. The book contains many diagrams and exercises to illustrate key points in the text.
Abstract This book provides a thorough introduction to the fascinating world of phase transitions as well as many related topics, including random walks, combinatorial problems, quantum field theory and S-matrix. Fundamental concepts of phase transitions, such as order parameters, spontaneous symmetry breaking, scaling transformations, conformal symmetry, and anomalous dimensions, have deeply changed the modern vision of many areas of physics, leading to remarkable developments in statistical mechanics, elementary particle theory, condensed matter physics and string theory. This self-contained book provides an excellent introduction to frontier topics of exactly solved models in statistical mechanics and quantum field theory, renormalization group, conformal models, quantum integrable systems, duality, elastic S-matrix, thermodynamics Bethe ansatz and form factor theory. The clear discussion of physical principles is accompanied by a detailed analysis of several branches of mathematics, distinguished for their elegance and beauty, such as infinite dimensional algebras, conformal mappings, integral equations or modular functions. Besides advanced research themes, the book also covers many basic topics in statistical mechanics, quantum field theory and theoretical physics. Each argument is discussed in great detail, paying attention to an overall coherent understanding of physical phenomena. Mathematical background is provided in supplements at the end of each chapter, when appropriate. The chapters are also followed by problems of different levels of difficulty. Advanced undergraduate and graduate students will find a rich and challenging source for improving their skills and for accomplishing a comprehensive learning of the many facets of the subject.