## Conformal Field TheoryConformal 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. |

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### Contents

Chapter I Conformal Symmetry and Fields | 1 |

Chapter II Representations of the Virasoro Algebra | 35 |

Chapter III Partition Functions and Bosonization | 83 |

Chapter IV AKM Algebras and WZNW Theories | 113 |

Chapter V Superconformal and SuperAKM Symmetries | 143 |

Chapter VI Coset Models | 169 |

Chapter VII W Algebras | 199 |

Chapter VIII Conformal Field Theory and Strings | 231 |

Chapter IX Quantum 2d Gravity and Topological Field Theories | 283 |

Chapter X CFT and Matrix Models | 317 |

Chapter XI CFT and Integrable Models | 351 |

Chapter XII Comments | 383 |

433 | |

Text Abbreviations | 475 |

477 | |

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### Common terms and phrases

2d gravity AKM algebra associated bosonic BRST central charge CFT's classical coefficients cohomology commutation conformal algebra conformal dimension conformal invariance conformal transformations consider constant constraints construction coordinates correlation functions corresponding coset covariant currents defined derivative differential operator eigenvalues equation equivalent fermionic field theory Fock space free field fusion rules gauge given Hamiltonian Hence highest weight holomorphic implies integral introduced irreps Ising model Kač Lie algebra Liouville theory matrix metric minimal models modular invariant NLSM non-trivial OPE's parameter particular partition function Phys physical primary fields quantization quantum group relations representation represented resp Riemann surface scalar field sect self-dual ſº solution space-time spin spinor stress tensor string theory structure superconformal superfield superspace superstring supersymmetric takes the form topological torus unitary vanishing vector vertex operators Virasoro algebra Weyl WZNW theory