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Gaussian free field and conformal field theory / Nam-Gyu Kang, Nikolai G. Makarov.

Abstract: 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...

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Bibliographic Details
Main Authors: Kang, Nam-Gyu (Author), Makarov, Nikolai G. (Author)
Format: Book
Language:English
Published: Paris : Société mathématique de France, 2013.
Series:Astérisque ; 353.
Subjects:
Conformal invariants.
Algebraic fields.
Gaussian distribution.
Table of Contents:
  • Fock space fields
  • Fock space fields as (very) generalized randon functions
  • Operator product expansion
  • Conformal geometry of Fock space fields
  • Stress tensor and Ward's identities
  • Ward's identities for finite Boltzmann-Gibbs ensembles
  • Virasoro field and representation theory
  • Existence of the Virasoro field
  • Operator algebra formalism
  • Modifications of the Gaussian free field
  • Current primary fields and KZ equations
  • Multivalued conformal Fock space fields
  • CFT ans SLE numerology
  • Connection to SLE theory
  • Vertex observables.

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