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This 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, with particular emphasis on vertex and face models. Special attention is given to explaining the underlying mathematical tools, including braid groups, knot invariants and towers of algebras. 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 super-conformal field theories. The book contains many diagrams and exercises to illustrate key points in the text. This book will be of interest to graduate students and researchers in theoretical physics and applied mathematics interested in integrable systems, string theory and conformal field theory.
List of contents
Preface; 1. S-matrices, spin chains and vertex models; 2. The Yang-Baxter equation - a first look; 3. Bethe ansatz - some examples; 4. The eight-vertex model; 5. Face models; 6. Quantum groups - mathematical review; 7. Integrable models at roots of unit; 8. Two-dimensional conformal field theories; 9. Duality in conformal field theories; 10. Coulomb gas representation; 11. Quantum groups in conformal field theory.
Summary
This 1996 book is an introduction to integrability and conformal field theory in two dimensions using quantum groups. It covers S-matrices, spin chains, vertex models, Yang–Baxter algebras, the Bethe ansatz, quantum groups, integrable models, two-dimensional conformal field theories and superconformal field theories. Many diagrams and exercises are included.
