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arXiv · hep-th/9709068

Duality in osp(1|2) Conformal Field Theory and link invariants

I. P. Ennes·P. Ramadevi·A. V. Ramallo·J. M. Sanchez de Santos
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Abstract

We study the crossing symmetry of the conformal blocks of the conformal field theory based on the affine Lie superalgebra osp(1|2). Within the framework of a free field realization of the osp(1|2) current algebra, the fusion and braiding matrices of the model are determined. These results are related in a simple way to those corresponding to the su(2) algebra by means of a suitable identification of parameters. In order to obtain the link invariants corresponding to the osp(1|2) conformal field theory, we analyze the corresponding topological Chern-Simons theory. In a first approach we quantize the Chern-Simons theory on the torus and, as a result, we get the action of the Wilson line operators on the supercharacters of the affine osp(1|2). From this result we get a simple expression relating the osp(1|2) polynomials for torus knots and links to those corresponding to the su(2) algebra. Further, this relation is verified for arbitrary knots and links by quantizing the Chern-Simons theory on the punctured two-sphere.

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I. P. Ennes, P. Ramadevi, A. V. Ramallo, J. M. Sanchez de Santos. 1997-12-23. Duality in osp(1|2) Conformal Field Theory and link invariants. https://doi.org/10.1142/s0217751x98001487

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