Lectures on Conformal Field Theory


  1. General coordinate, Weyl and Conformal invariance. Conformal group in D > 2 dimensions.
  2. Conformal group in 2D. The Witt algebra. PSL(2,C). Introducing CFT: cylinder and plane. Radial quantization.
  3. Example of CFT: free massless boson. OPE, holomorphic normal ordering.
  4. Ward identities. Examples.
  5. Energy-momentum tensor. Scaling dimensions. Primary fields. Examples. TT-OPE, central charge.
  6. Virasoro algebra. "Commutator-residue" identities.
  7. Mode expansions.
  8. Highest weight states of Virasoro algebra,
  9. Representations of Virasoro algebra, Kac determinant, unitarity, c=1, c=0 representations.
  10. Correlation functions. Conformal Ward identity. PSL(2,C) invariance.
  11. 2,3,4-point correlation functions. The use of PSL(2,C) invariance.
  12. OPE and correlation functions. Conformal blocks. Introduction to Moore-Seiberg theory: Fusing-Braiding relations.
  13. Another look on Kac determinant. Singular (Null) vectors. Constraints on OPE.
  14. Kac table, Minimal models
  15. Applications of CFT to Condenced Matter Physics.
  16. CFT on a torus. Modular invariance.
  17. Free massless fermion: Ramond and Neveu-Schwarz sectors. Modular invariant partition function. Identification with critical Ising model.
  18. Verlinde formula for fusion rules.
  19. Extensions of Virasoro algebra. WZNW theories, Superconformal algebras, W-algebras.
  20. Detailed study of WZNW theory. Knizhnik-Zamolodchikov equation.
  21. Coset theories.
  22. Another look on Moore-Seiberg theory. Vafa relation. Rational CFT.
  23. ...Advanced topics.

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