Extended conformal symmetry in two-dimensional quantum field theory
In a given model of conformal field theory (CFT) the true symmetry algebra is larger than the conformal algebra only. The description of such models can be improved by studying the extra symmetry. One may study extended symmetries by proposing a number of extra generators and closing the algebra. The ultimate aim in this point of view would be to classify all CFT's within a certain class. Once a consistent algebra has been found such that the proposed algebra is associative, one can try to find representations realizing the symmetry. It is the main purpose of chapter 2 and chapter 4 to study non-linear higher spin extensions of the Virasoro algebra, W-algebras, in specific models of CFT. In chapter 2, the author constructs an N=1 super W[sub 3] algebra, which is the generic c = 4(1-(18/[(m+3)(m+6)])) supersymmetric coset model based on (A[sup 1][sub 2] [circle plus]A[sup 1][sub 2], A[sup 1][sub 2]) at level (3,m). In the first model of this series, which has c = 10/7, the algebra reduces to the minimal super W[sub 3] algebra. It is possible to get a set of 8 generating supercurrents of this algebra for the m [yields] [infinity] limit model of this series. The author will argue that the complete set of supercurrents in the full super W[sub 3] algebra should contain at least the above-mentioned 8 supercurrents. In chapter 3, the author shows how the parameterization of SU(2)xU(1) in terms of a chiral superfield [Phi] and a twisted chiral superfield [Lambda] leads to N=2 supersymmetric WZW model. The model possesses an N=4 superconformal symmetry. The author exhibits explicit formulas for the generators of the full N=4 superconformal current algebra in terms of N=2 affine Kac-Moody currents. In chapter 4, the author focuses on the m [yields] [infinity] limit of the unitary minimal series c(WB[sub 2]) = 5/2(1 - (12/[(m+3)(m+4)])) based on the cosets (B[sub 2][circle plus]B[sub 2], B[sub 2]) at level (1,m).
- Research Organization:
- State Univ. of New York, Stony Brook, NY (United States)
- OSTI ID:
- 7073157
- Resource Relation:
- Other Information: Thesis (Ph.D.)
- Country of Publication:
- United States
- Language:
- English
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