| 《onformal Field Theory Vol.2(共形场论)》可作为高等院校理论物理和数学专业高年级本科生和研究生教材，也可供物理学和数学等相关学科研究人员参考。对于这些领域的研究人员和高校师生，这是一本不可多得的参考书。 |
| 8.A.3 The Singular Vectors |hr，s+rs”>：General Strategy 8.A.4，the Leading ActionofA△ r，1 8.A.5 Fusion at Work 8.A.6 The Singular Vectors |hr，s+rs>：Summary Exercises 9 The Coulomb-Gas Formalism 9.1 Vertex Operators 9.1.1 Corrclators of Vertex Operators 9.1.2 the Neutrality Condition 9.1.3 the Back ground Charge 9.1.4 the AnomalOUS OPES 9.2 Screening Operators 9.2.1 Physical and Vertex Operators 9.2.2 Minimal Models 9.2.3 Four-POint Functions：Sample Correlators 9.3 Minimal Models：General Structure of Correlation Functions 9.3.1 Conformal Blocks for the Four-Point Functions 9.3.2 Conformal Blocks for the N-Point Function on the Plane 9.3.3 Monodromy and Exchange Relations for Conformal Blocks 9.3.4 Conformal Blocks for Corrclators on a Surface of Arbitrary Genus 9.A Calculation of the Energy-Momentum Tensor 9.B Screened Vertex Operators and BRST Cohomology：A Proof of the Coulomb-Gas Representation Of Minimal Models 9.B.1 Charged Bosonic Fock Spaces and Their Virasoro Structure 9.B.2 Screened Vertex Operators 9.B.3 The BRST Charge 9.B.4 BRST Invariance and Cohomology 9.B.5 The Coulomb-Gas Representation Exercises 10 Modular Invariance 10.1 C0nformal Field Theory on the Torus 10.1.1 The Partition Function 10.1.2 Modular Invariance 10.1.3 Generators and the Fundamental Domain 10.2 The Free Boson on the Torus 10.3 Free Fermions on the Torus 10.4 Models with C=1 10.4.1 Compactified Boson 10.4.2 Multi-Component Chiral Boson 10.4.3 Orbifold 10.5 Minimal Models：Modular Invariance and operater Content 10.6 Minimal Models：Modular Transformations of the Characters 10.7 MinimaI Models：Modular lnvariant Partition Funcfions 10.7.1 Diagonal Modular Invariants 10.7.2 Nondiagonal Modular Invariants：Example of the Three-state Potts Model 10.7.3 Block-Diagonal Modular Invariants 10.7.4 Nondiagonal Modular Invariants Related to an Automorphism 10.7.5 D Seriesfrom Z2 OrbifoldS 10.7.6 The Classification of Minimal Models 10.8 Fusion Rules and Modular Invariance 10.8.1 verlindeS Formula for Minimal Theories 10.8.2 Counting Conformal Blocks 10.8.3 A General Proof of Verlindes Formula 10.8.4 Extended Symmetries and Fusion Rules 10.8.5 Fusion Rules of the Extended Theory of the Three-State Potts Model 10.8.6 A Simple Example of Nonminimal Extended Theory：The Free Boson at the Self-Dual Radius 10.8.7 Rational Conformal Field Theory：A Definition 10.A Theta Functions 10.A.1 The Jacobi Tripie Product 10.A.2 Theta Functions 10.A.3 DedekindS n Funcfion 10.A.4 Modular Transformations of Theta Functions 10.A.5 Doubling Identities Exercises 11 Finite-Size Scaling and Boundaries 11.1 Conformal Invariance on a Cylinder 11.2 Surface Critical Behavior 11.2.1 Conforrnal Field rnleory on the Upper Half-Plane 11.2.2 The Ising Model on the Upper Half-Plane 11.2.3 The Infinite Strip 11.3 Boundary Operators 11.3.1 Introduction 11.3.2 Boundary States and the Verlinde Formula 11.4 Critical Percolation 11.4.1 Statement of the Problem 11.4.2 Bond Percolation and the Q-state POtts Model 11.4.3 Boundary Operators and Crossing Probabilities Exercises 12 The Two-Dimensional Ising Modd 12.1 The Statistical Model 12.2 The Underlying Fermionic Theory 12.2.1 Fermion：Energy and Energy-Momentum Tensor 12.2.2 Spin 12.3 Correlation Functions on the Plane by Bosonization 12.3.1 the Bosonization Rules 12.3.2 Energy Correlators 12.3.3 Spin and General Correlators 12.4 The Ising Model on the Torus 12.4.1 The Partition Function 12.4.2 General Ward Identifies on the Torus 12.5 Correlation Functions on the Torus 12.5.1 Flermion and Energy Correlators 12.5.2 Spin and Disorder-Field Correlators 12.6 Bosonization on the Torus 12.6.1 The Tw0 Bosonizations of the Ising Model：Partition Functions and Operators 12.6.2 Compactified Boson Correlations on the Plane and or the Torus 12.6.3 Ising Correlators from the Bosonization of the Dirac Fermion 12.6.4 Ising Correlators from the Bosonization of Two Real Fermions 12.A Elliptic and Treta Function Identities 12.A.1 Generalities on Elliptic Functions 12.A.2 Periodicity and ZeroS of the Jacobi Theta Functions 12.A.3 Doubling Identifies Exercises Part C CONOFRMAL FIELD THEORIES WITH LIE-GROUP SYMMETRY 13 Simple Lie Algebras 13.1 The Structure of Simple Lie Algebras 13.1.1 TheCartan-Wevl Basis 13.1.2 The Killing Form 13.1.3 Weigllts 13.1.4 Simple Roots and the Caftan Matrix 13.1.5 The Chevalley Basis 13.1.6 Dynkin Diagrams 13.1.7 Fundamental Weights 13.1.8 TheWeyl Group 13.1.9 Lattices 13.1.10 Normalization Convention 13.1.11 Examples 13.2 Highest-Weight Representations 13.2.1 Weights and Their Multiplicities l3.2.2 Conjugate Representations 13.2.3 Quadratic Casimir Operator 13.2.4 Index of a Representation 13.3 Tableaux and Patterns (su(N)) 13.3.1 Young Tableaux 13.3.2 Partitions and Orthonormal Bases 13.3.3 Semistandard Tableaux 13.3.4 Gelfand-Tsetlin Paaerns 13.4 Characters 13.4.1 WleylS Character Formula 13.4.2 The Dimension and the Strange Formulae 13.4.3 Schur Functions 13.5 Tensor Products：Computational Tools 13.5.1 The Character Method 13.5.2 Algorithm for the Calculation of Tensor Products 13.5.3 The Littlewood-Rchardson Rule 13.5.4 Berenstein-Zelevinsky Triangles 13.6 Tensor Products：A Fusion-Rule Point of View 13.7 Algebra Embeddings and Branching Rules 13.7.1 Embedding Index 13.7.2 Classification of Embeddings 13.A Properties of Simple Lie Algebras 13.B Notation for Simple Lie Algebras Exercises 14 Affine Lie Algebras 14.1 The Structure Of AfIine Lie Algebras 14.1.1 From Simple Lie Algebras to Affine Lie Algebras 14.1.2 The killing Form 14.1.3 Simple Roots，the Cartan Matrix and Dynkin Diagrams 14.1.4 The ChevalIcy Basis 14.1.5 Fundamental Weights 14.1.6 The Affine Weyl Group 14.1.7 Examples 14.2 Outer Automorphisms 14.2.1 Symmetry of the Extended Diagram and Group of Outer Auto morphisms 14.2.2 Action of Outer Automorphisms on Wleights …… 15 WZW Models 16 Fusion Rules in WZW Models 17 Modular Invariants in WZW Models 18 Cosets References Index |
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