Understanding conformal field theory through parafermions and Chern Simons theory

Thesis/Dissertation · Thu Nov 19 04:00:00 EST 1992

DOI:https://doi.org/10.2172/10140828· OSTI ID:10140828

Hotes, Scott A. ^[1]

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1. 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
• Country of Publication: United States
• Language: English

Related Subjects

662110
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CONFORMAL GROUPS
FERMIONS
MONOPOLES
QUANTUM FIELD THEORY
THEORY OF FIELDS AND STRINGS
TWO-DIMENSIONAL CALCULATIONS