TY  - BOOK
AU  - Kang,Nam-Gyu
AU  - Makarov,Nikolai G.
TI  - Gaussian free field and conformal field theory
T2  - Asterisque
SN  - 9782856293690 (print)
U1  - 510=4 23
PY  - 2013///
CY  - Paris, France
PB  - Societe mathematique de France
KW  - Conformal invariants
KW  - Algebraic fields
KW  - Gaussian distribution
N1  - "Publie avec le concours du Centre national de la recherche scientifique."; Includes bibliographical references (pages 131-134) and index; Introduction--
1. Fock space fields --
2. Fock space fields as (very) generalized random functions --
3. Operator product expansion --
4. Conformal geometry of Fock space fields --
5. Stress tensor and Ward's identities --
6. Ward's identities for finite Boltzmann-Gibbs ensembles --
7. Virasoro field and representation theory --
8. Existence of the Virasoro field --
9. Operator algebra formalism --
10. Modifications of the Gaussian free field --
11. Current primary fields and KZ equations --
12. Multivalued conformal Fock space fields --
13. CFT ans SLE numerology --
14. Connection to SLE theory --
15. Vertex observables--
Bibliography--
Index
N2  - "In these mostly expository lectures, we give an elementary introduction to conformal field theory in the context of probablility theory and complex analysis.  We consider statistical fields, and define Ward functionals in terms of their Lie derivatives.  Based on this approach, we explain some equations of conformal field theory and outline their relation to SLE theory."--Page iii
ER  -