Understanding conformal field theory through parafermions and Chern Simons theory
- Univ. of California, Berkeley, CA (United States)
Conformal field theories comprise a vast class of exactly solvable two dimensional quantum field theories. Conformal theories with an enlarged symmetry group, the current algebra symmetry, axe a key ingredient to possible string compactification models. The following work explores a Lagrangian approach to these theories. In the first part of this thesis, a large class of conformal theories, the so-called coset models, are derived semi-classically from a gauged version Of the Wess-Zumino-Witten functional. A non-local field transformation to the parafermionic field description is employed in the quantization procedure. Classically, these parafermionic fields satisfy non-trivial Poisson brackets, providing insight into the fractional spin nature of the conformal theory. The W-algebra symmetry is shown to appear naturally in this approach. In the second part of this thesis, the connection between the fusion algebra structure of Wess-Zumino-Witten models and the quantization of the Chern-Simons action on the torus is made explicit. The modular properties of the conformal model are also derived in this context, giving a natural demonstration of the Verlinde conjecture. The effects of background gauge fields and monopoles are also discussed.
- Research Organization:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Organization:
- USDO; National Science Foundation (NSF)
- DOE Contract Number:
- AC03-76SF00098
- OSTI ID:
- 10140828
- Report Number(s):
- LBL-33186; ON: DE93010452; CNN: Grant PHY90-21139
- Resource Relation:
- Other Information: TH: Thesis (Ph.D.); PBD: 19 Nov 1992
- Country of Publication:
- United States
- Language:
- English
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