Titlebook: Conformal Field Theory; Philippe Francesco,Pierre Mathieu,David Sénéchal Textbook 1997 Springer-Verlag New York, Inc. 1997 High-Energy Phy

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Conformal Invariance in Two Dimensionsre exists in two dimensions an infinite variety of coordinate transformations that, although not everywhere well-defined, are locally conformal: they are holomorphic mappings from the complex plane (or part of it) onto itself. Among this infinite set of mappings one must distinguish the 6-parameter

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The Operator Formalismfunctions known as the Ward identities. These Ward identities were most easily expressed in the form of an operator product expansion of the energy-momentum tensor with local fields. It was implicit, however, that operator product expansions were occurring within correlation functions and no use was

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Minimal Models Iormal theories called .. These theories are characterized by a Hilbert space made of a . number of representations of the Virasoro algebra (Verma modules); in other words, the number of conformal families is finite. Such theories describe discrete statistical models (e.g., Ising, Potts, and so on) a

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The Coulomb-Gas Formalismundary conditions. This representation bears the name of . or .. This terminology comes from the resemblance of the free boson correla . with the electric potential energy between two unit charges in two dimensions. In Sect. 9.1, we calculate the correlation function of vertex operators and indicate

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Affine Lie Algebraser having introduced the affine Lie algebras per se, we show how the fundamental concepts of roots, weights, Cartan matrices, and Weyl groups are extended to the affine case. Section 14.2 introduces the outer automorphism group of affine Lie algebras, which is generated by the new symmetry transform

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