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Three-dimensional Chern-Simons theory as a theory of knots and links

1991/11/28 by R. K. Kaul, R.K. Kaul, T. R. Govindarajan +1
Mathematics · Physics and Astronomy · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological Materials and Phenomena #hep-th #math.QA

paper · pdf · doi:10.1016/0550-3213(92)90524-f

published as Nucl.Phys. B380 (1992) 293-336 · 45 pages (without figures)

arxiv created 1991/11/28 · openalex publication_date 1992/08/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Three dimensional SU(2) Chern-Simons theory has been studied as a topological field theory to provide a field theoretic description of knots and links in three dimensions. A systematic method has been developed to obtain the link-invariants within this field theoretic framework. The monodromy properties of the correlators of the associated Wess-Zumino SU(2)k conformal field theory on a two-dimensional sphere prove to be useful tools. The method is simple enough to yield a whole variety of new knot invariants of which the Jones polynomials are the simplest example.

Citations