## Conformal Field TheoryFilling 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. |

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### Contents

3 | |

15 | |

Statistical Mechanics | 60 |

Global Conformal Invariance 95 | 94 |

Conformal Invariance in Two Dimensions | 111 |

The Operator Formalism | 150 |

Minimal Models I | 200 |

Minimal Models II | 239 |

The TwoDimensional Ising Model | 439 |

Simple Lie Algebras | 489 |

Affine Lie Algebras | 556 |

WZW Models | 617 |

Fusion Rules in WZW Models | 675 |

Modular Invariants in WZW Models | 719 |

Šu3 | 766 |

Cosets | 797 |

The CoulombGas Formalism | 294 |

the CoulombGas Representation of Minimal Models | 320 |

Modular Invariance | 335 |

FiniteSize Scaling and Boundaries | 409 |

860 | |

877 | |

### Other editions - View all

Conformal Field Theory Philippe Francesco,Philippe Di Francesco,Pierre Mathieu,David Sénéchal,David Senechal Limited preview - 1997 |

### Common terms and phrases

action affine Lie algebras antiholomorphic associated boson boundary conditions branching rules calculation Cartan central charge characters conformal blocks conformal dimension conformal field theory conformal invariance conformal transformations conjugate constraints correlation functions corresponding decomposition defined denote derive diagonal differential equation Dynkin diagrams Dynkin labels eigenvalue elements embedding energy energy-momentum tensor equivalent expression factor fermion finite fixed free boson fusion rules Hamiltonian highest weight holomorphic integrable Ising model lattice matrix minimal models modular invariants modular transformation multiplicity obtained orbifold outer automorphisms partition function permutation polynomial Potts model primary fields quantum result Sect simple roots singular vector space spin su(N subalgebra symmetry tableau tensor product torus two-point function unitary vacuum vanishes variables Verma module vertex operators Virasoro algebra Ward identity Weyl group WZW models zero