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| Introduction | |
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| Basics in Conformal Field Theory | |
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| he Conformal Group | |
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| Conformal Invariance | |
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| Conformal Group in d ? 3 | |
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| Conformal Group in d ? 2 | |
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| Primary Fields | |
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| The Energy-Momentum Tensor | |
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| Radial Quantisation | |
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| The Operator Product Expansion | |
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| Operator Algebra of Chiral Quasi-Primary Fields | |
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| Conformal Ward Identity | |
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| Two- and Three-Point Functions | |
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| General Form of the OPE for Chiral Quasi-Primary Fields | |
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| Normal Ordered Products | |
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| The CFT Hilbert Space | |
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| Simple Examples of CFTs | |
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| The Free Boson | |
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| The Free Fermion | |
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| The (b,c) Ghost Systems | |
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| Highest Weight Representations of the Virasoro Algebra | |
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| Correlation Functions and Fusion Rules | |
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| Non-Holomorphic OPE and Crossing Symmetry | |
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| Fusing and Braiding Matrices | |
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| Further Reading | |
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| Symmetries of Conformal Field Theories | |
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| Ka?-Moody Algebras | |
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| The Sugawara Construction | |
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| Highest Weight Representations of S�(2)k | |
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| The S�(N)1 Current Algebra | |
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| The Knizhnik-Zamolodchikov Equation | |
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| Coset Construction | |
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| W Algebras | |
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| Further Reading | |
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| Conformal Field Theory on the Torus | |
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| The Modular Group of the Torus and the Partition Function | |
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| Examples for Partition Functions | |
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| The Free Boson | |
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| The Free Boson on a circle | |
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| The Free Boson on a circle of Radius R=?2k | |
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| The Free Fermion | |
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| The Free Boson Orbifold | |
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| The Verlinde Formula | |
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| The S�(2)k Partition Functions | |
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| Modular Invariants of Virc<1 | |
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| The Parafermions | |
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| Simple Currents | |
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| Additional Topics | |
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| Asymptotic Growth of States in RCFTs | |
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| Dilogarithm Identities | |
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| Further Reading | |
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| Supersymmetric Conformal Field Theory | |
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| N=1 Superconformal Models | |
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| N=2 Superconformal Models | |
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| Chiral Ring | |
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| Spectral Flow | |
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| Coset Construction for the N ? 2 Unitary Series | |
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| Gepner Models | |
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| Massless Models of Gepner Models | |
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| Further Reading | |
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| Boundary Conformal Field Theory | |
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| The Boson with Boundaries | |
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| Boundary Conditions | |
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| Partition Function | |
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| Boundary States for the Free Boson | |
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| Boundary Conditions | |
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| Tree-Level Amplitudes | |
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| Boundary States for RCFTs | |
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| CFTs on Non-Orientable Sufraces | |
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| Crosscap States for the Free Boson | |
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| Crosscap States for RCFTs | |
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| he Orientifold of the Bosonic String | |
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| Further Reading | |
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| Concluding Remarks | |
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| General Books on CFT and String Theory259 | |
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| Index | |