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

By: Contributor(s): Material type: TextTextSeries: Asterisque ; 353.Publication details: Paris, France : Societe mathematique de France, 2013.Description: vii, 136 p. : illustrations ; 24 cmISBN:
  • 9782856293690 (print)
Subject(s): DDC classification:
  • 510=4 23 As853
Contents:
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.
Summary: "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.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 510=4 As853 (Browse shelf(Opens below)) Available C26460
Total holds: 0

"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.

"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.

In English ; with abstract in French.

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