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 Astérisque 2013; 136 pp; softcover Number: 353 ISBN-13: 978-2-85629-369-0 List Price: US$52 Member Price: US$41.60 Order Code: AST/353 In these mostly expository lectures, the authors give an elementary introduction to conformal field theory in the context of probability theory and complex analysis. The authors consider statistical fields and define Ward functionals in terms of their Lie derivatives. Based on this approach, the authors explain some equations of conformal field theory and outline their relation to SLE theory. A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list. Readership Graduate students and research mathematicians interested in conformal field theory and Schramm-Loewner Evolution. Table of Contents Introduction Lecture 1. Fock space fields Appendix 2. Fock space fields as (very) generalized random functions Lecture 3. Operator product expansion Lecture 4. Conformal geometry of Fock space fields Lecture 5. Stress tensor and Ward's identities Appendix 6. Ward's identities for finite Boltzmann-Gibbs ensembles Lecture 7. Virasoro field and representation theory Appendix 8. Existence of the Virasoro field Appendix 9. Operator algebra formalism Lecture 10. Modications of the Gaussian free field Appendix 11. Current primary fields and KZ equations Lecture 12. Multivalued conformal Fock space fields Appendix 13. CFT and SLE numerology Lecture 14. Connection to SLE theory Lecture 15. Vertex observables Bibliography Index