Introduction / 1: |
Basics in Conformal Field Theory / 2: |
he Conformal Group / 2.1: |
Conformal Invariance / 2.1.1: |
Conformal Group in d ? 3 / 2.1.2: |
Conformal Group in d ? 2 / 2.1.3: |
Primary Fields / 2.2: |
The Energy-Momentum Tensor / 2.3: |
Radial Quantisation / 2.4: |
The Operator Product Expansion / 2.5: |
Operator Algebra of Chiral Quasi-Primary Fields / 2.6: |
Conformal Ward Identity / 2.6.1: |
Two- and Three-Point Functions / 2.6.2: |
General Form of the OPE for Chiral Quasi-Primary Fields / 2.6.3: |
Normal Ordered Products / 2.7: |
The CFT Hilbert Space / 2.8: |
Simple Examples of CFTs / 2.9: |
The Free Boson / 2.9.1: |
The Free Fermion / 2.9.2: |
The (b,c) Ghost Systems / 2.9.3: |
Highest Weight Representations of the Virasoro Algebra / 2.10: |
Correlation Functions and Fusion Rules / 2.11: |
Non-Holomorphic OPE and Crossing Symmetry / 2.12: |
Fusing and Braiding Matrices / 2.13: |
Further Reading |
Symmetries of Conformal Field Theories / 3: |
Ka?-Moody Algebras / 3.1: |
The Sugawara Construction / 3.2: |
Highest Weight Representations of Sû(2)k / 3.3: |
The Sô(N)1 Current Algebra / 3.4: |
The Knizhnik-Zamolodchikov Equation / 3.5: |
Coset Construction / 3.6: |
W Algebras / 3.7: |
Conformal Field Theory on the Torus / 4: |
The Modular Group of the Torus and the Partition Function / 4.1: |
Examples for Partition Functions / 4.2: |
The Free Boson on a circle / 4.2.1: |
The Free Boson on a circle of Radius R=?2k / 4.2.3: |
The Free Boson Orbifold / 4.2.4: |
The Verlinde Formula / 4.3: |
The Sû(2)k Partition Functions / 4.4: |
Modular Invariants of Virc<1 / 4.5: |
The Parafermions / 4.6: |
Simple Currents / 4.7: |
Additional Topics / 4.8: |
Asymptotic Growth of States in RCFTs / 4.8.1: |
Dilogarithm Identities / 4.8.2: |
Supersymmetric Conformal Field Theory / 5: |
N=1 Superconformal Models / 5.1: |
N=2 Superconformal Models / 5.2: |
Chiral Ring / 5.3: |
Spectral Flow / 5.4: |
Coset Construction for the N ? 2 Unitary Series / 5.5: |
Gepner Models / 5.6: |
Massless Models of Gepner Models / 5.7: |
Boundary Conformal Field Theory / 6: |
The Boson with Boundaries / 6.1: |
Boundary Conditions / 6.1.1: |
Partition Function / 6.1.2: |
Boundary States for the Free Boson / 6.2: |
Tree-Level Amplitudes / 6.2.1: |
Boundary States for RCFTs / 6.3: |
CFTs on Non-Orientable Sufraces / 6.4: |
Crosscap States for the Free Boson / 6.5: |
Crosscap States for RCFTs / 6.6: |
he Orientifold of the Bosonic String / 6.7: |
Concluding Remarks |
General Books on CFT and String Theory|259 |
Index |
Introduction / 1: |
Basics in Conformal Field Theory / 2: |
he Conformal Group / 2.1: |