School of Mathematics and Statistics - Theses
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ItemCoset construction for the N=2 and osp(1|2) minimal models( 2019)The thesis presents the study of the N=2 and osp(1|2) minimal models at admissible levels using the method of coset constructions. These sophisticated minimal models are rich in mathematical structure and come with various interesting features for us to investigate. First, some general principles of conformal field theory are reviewed, notations used throughout the thesis are established. The ideas are then illustrated with three examples of bosonic conformal field theories, namely, the free boson, the Virasoro minimal models, and the admissible-level Wess-Zumino-Witten models of affine sl(2). The concept of supersymmetry is then introduced, and examples of fermionic conformal field theories are discussed. Of the two minimal models of interest, the N=2 minimal model, tensored with a free boson, can be extended into an sl(2) minimal model tensored with a pair of fermionic ghosts, whereas an osp(1|2) minimal model is an extension of the tensor product of certain Virasoro and sl(2) minimal models. We can therefore induce the known structures of the representations of the coset components and get a rather complete picture for the minimal models we want to investigate. In particular, the irreducible highest-weight modules (including the relaxed highest-weight modules, which result in a continuous spectrum) are classified, their characters and Grothendieck fusion rules are computed. The genuine fusion products and the projective covers of the irreducibles are conjectured. The thesis concludes with a vision of how this method can be used for the study of other affine superalgebras. This provides a promising approach to solving superconformal field theories that are currently little known in the literature.The thesis presents the study of the N=2 and osp(1|2) minimal models at admissible levels using the method of coset constructions. These sophisticated minimal models are rich in mathematical structure and come with various interesting features for us to investigate. First, some general principles of conformal field theory are reviewed, notations used throughout the thesis are established. The ideas are then illustrated with three examples of bosonic conformal field theories, namely, the free boson, the Virasoro minimal models, and the admissible-level Wess-Zumino-Witten models of affine sl(2). The concept of supersymmetry is then introduced, and examples of fermionic conformal field theories are discussed. Of the two minimal models of interest, the N=2 minimal model, tensored with a free boson, can be extended into an sl(2) minimal model tensored with a pair of fermionic ghosts, whereas an osp(1|2) minimal model is an extension of the tensor product of certain Virasoro and sl(2) minimal models. We can therefore induce the known structures of the representations of the coset components and get a rather complete picture for the minimal models we want to investigate. In particular, the irreducible highest-weight modules (including the relaxed highest-weight modules, which result in a continuous spectrum) are classified, their characters and Grothendieck fusion rules are computed. The genuine fusion products and the projective covers of the irreducibles are conjectured. The thesis concludes with a vision of how this method can be used for the study of other affine superalgebras. This provides a promising approach to solving superconformal field theories that are currently little known in the literature.