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Gaussian Free Field and Conformal Field Theory
Nam-Gyu Kang, Seoul National University, Republic of Korea, and Nikolai G. Makarov, California Institute of Technology, Pasadena, CA
A publication of the Société Mathématique de France.
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
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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.


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
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