共形场论 第1卷(英文影印版)

.5.1 the conformal group in two dimensions
5.2 ward identifies
5.3 free fields and the operator product expansion
5.4 the central charge
5.a the trace anomaly
5.b the heat kemel
6 the operator formalism
6.1 the operator formalism of conformal field theory
6.2 the virasoro algebra
6.3 the free boson
6.4 the free fermion
6.5 normal ordering
6.6 conformal families and operator algebra
7 minimal models i
7.1 verma modules
7.2 the kac determinant
7.3 overview of minimal models
7.4 examples
8 minimal models ii
8.1 irreducible modules and minimal characters
8.2 explicit form of singular vectors
8.3 differential equations for the correlation functions
8.4 fusion rules
9 the coulomb-gas formalism
9.1 vertex operators
9.2 screening operators
9.3 minimal models: general structure of correlation functions
i0 modular lavarianee
10.1 conformal field theory on the toms
10.2 the free boson on the toms
10.3 free fermions on the toms
10.4 models withc = 1
10.5 minimal models: modular invariance and operator content
10.6 minimal models: modular transformations of the characters
10.7 minimal models: modular invariam partition functions
10.8 fusion rules and modular invariance..
11 finite-size scaling and
11.1 conformal invariance on a cylinder
11.2 surface critical behavior
11.3 boundary operators
11.4 critical perators
12 the two-dimensional ising model
12.1 the statistical model
12.2 the underlying fermionic theory
12.3 correlation functions on the plane by bosonization
12.4 the ising-model on the toms
12.5 correlation functions on the toms
12.6 bosonization on the toms
part c conformal field theories with lie-group
symmetry
13 simple lie algebras
13.1 the structure of simple lie algebras
13.2 highest-weight representations
13.3 tableaux and patterns (su(n))
13.4 characters
13.5 tensor products: computational tools
13.6 tensor products: a fusion-rule point of view
13.7 algebra embeddings and branching rules
14 affine lie algebras
14.1 the structure of affine lie algebras
14.3 highest-weight representatiom
14.4 characters
14.5 modular transformations
14.6 properties of the modular $ matrix
14.7 affine embeddings
15 wzw models
15.1 introducing wzw models
15.2 the sugawara construction
15.3 wzw primary fields
15.4 four-point functions and the knithniir-zamolodchikov equation
15.5 free-fermion representations
15.6 vertex representations
15.7 the wakimoto free-field representation
16 fusion rules in wzw models
16.1 symmetries of fusion coefficients
16.2 fusion rules using the affine weyl group
16.3 quantum dimensions
16.4 the depth rule and threshold levels
16.5 fusion potentials (su(n))
16.6 level-rank duality
16.7 modular invarinnts in wzw models
17.1 modular invariance in wzw models
17.2 a simple nondiagonal modular invariant
17.3 modular lnvariants using outer automorphisms
17.4 the su(2)4 nondiagonal invariant revisited
17.5 conformal embeddings
17.6 modular invariants from conformal embeddings
17.7 some classification results
17.8 permutation invariants and extended chiral algebras
17.9 galois synunetry
17.10 modular invariants, generalized ade diagrams and fusion rules
18 cosets
18.1 the coset consuuction
18.2 branching functions and characters
18.3 coset description of unitary minimal models
18.4 other coset representations of minimal models
18.5 the coset sy(2)ku(1) and parafermions
18.6 conformal theories with fractional su(2) spectrum- generating algebra
18.7 coset description of nonunitary minimal models
references
index...