Topics in two dimensional conformal field theory and three dimensional topological lattice field theory
The authors first construct new parafermions in two-dimensional conformal field theory, generalizing the Z{sub L} parafermion theories from integer L to rational L. These non-unitary parafermions have some novel features: an infinite number of currents with negative conformal dimensions for most (if not all) of them. String functions of these new parafermion theories are calculated. They also construct new representations of N = 2 superconformal field theories, whose characters are obtained in terms of these new string functions. They then generalize Felder`s BRST cohomology method to construct the characters and branching functions of the SU(2){sub L} {times} SU(2){sub K}/SU(2){sub K+L} coset theories, where one of the (K,L) is an integer. This method of obtaining the branching functions also serves as a check of their new Z{sub L} parafermion theories. The next topic is the Lagrangian formulation of conformal field theory. They construct a chiral gauged WZW theory where the gauge fields are chiral and belong to the subgroups H{sub L} and H{sub R}, which can be different groups. This new construction is beyond the ordinary vector gauged WZW theory, whose gauge group H is a subgroup of both G{sub L} and G{sub R}. In the special case where H{sub L} = H{sub R}, the quantum theory of chiral gauged WZW theory is equivalent to that of the vector gauged WZW theory. It can be further shown that the chiral gauged WZW theory is equivalent to [G{sub L}/H{sub L}](z) {direct_product} [G{sub R}/H{sub R}]({bar z}) coset models in conformal field theory. In the second half of this thesis, they construct topological lattice field theories in three dimensions. After defining a general class of local lattice field theories, they impose invariance under arbitrary topology-preserving deformations of the underlying lattice, which are generated by two local lattice moves. Invariant solutions are in one-to-one correspondence with Hopf algebras satisfying a certain constraint.
- Research Organization:
- Cornell Univ., Ithaca, NY (United States)
- OSTI ID:
- 39343
- Resource Relation:
- Other Information: TH: Thesis (Ph.D.); PBD: 1993
- Country of Publication:
- United States
- Language:
- English
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