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.

Table of Contents

Part A INTRODUCTION

1 Introduction

2 Quantum Field Theory

3 Statistical Mechanics

Part B FUNDAMENTALS

4 Global Conformal Invariance

5 Conformal Invariance in Two Dimensions

6 The Operator Formalism

7 Minimal Models I

8 Minimal Models II

9 The Coulomb-Gas FormaUsm

10 Modular Invariance

11 Finite-Size Scaling and Boundaries

12 The Two-Dimensional Ising Model

Part C CONFORMAL FIELD THEORIES WITH LIE-GROUP SYMMETRY

13 Simple Lie Algebras

14 Affine Lie Algebras

15 WZW Models

16 Fusion Rules in WZW Models

17 Modular Invariants in WZW Models

18 Cosets