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Title: Understanding conformal field theory through parafermions and Chern Simons theory

Abstract

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.

Authors:
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE; National Science Foundation (NSF); USDOE, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
OSTI Identifier:
6653388
Report Number(s):
LBL-33186
ON: DE93010452; CNN: PHY90-21139
DOE Contract Number:  
AC03-76SF00098
Resource Type:
Technical Report
Resource Relation:
Other Information: Thesis (Ph.D.)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; QUANTUM FIELD THEORY; CONFORMAL GROUPS; FERMIONS; MONOPOLES; TWO-DIMENSIONAL CALCULATIONS; FIELD THEORIES; LIE GROUPS; SYMMETRY GROUPS; 662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)

Citation Formats

Hotes, S A. Understanding conformal field theory through parafermions and Chern Simons theory. United States: N. p., 1992. Web. doi:10.2172/6653388.
Hotes, S A. Understanding conformal field theory through parafermions and Chern Simons theory. United States. https://doi.org/10.2172/6653388
Hotes, S A. 1992. "Understanding conformal field theory through parafermions and Chern Simons theory". United States. https://doi.org/10.2172/6653388. https://www.osti.gov/servlets/purl/6653388.
@article{osti_6653388,
title = {Understanding conformal field theory through parafermions and Chern Simons theory},
author = {Hotes, S A},
abstractNote = {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.},
doi = {10.2172/6653388},
url = {https://www.osti.gov/biblio/6653388}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Thu Nov 19 00:00:00 EST 1992},
month = {Thu Nov 19 00:00:00 EST 1992}
}