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New hierarchies of knot polynomials from topological Chern-Simons gauge theory
Authors:Kengo Yamagishi  Mo-Lin Ge  Yong-Shi Wu
Institution:(1) Department of Physics, University of Utah, 84112 Salt Lake City, UT, U.S.A.;(2) Theoretical Physics, Nankai Institute of Mathematics, Nankai University, Tianjin, P.R. China;(3) Department of Physics, University of Utah, 84112 Salt Lake City, UT, U.S.A.
Abstract:In this Letter, we report on a study of the expectation values of Wilson loops in D=3 topological Chern-Simons theory associated with the fundamental representation of the simple Lie algebras SO(n) and Sp(n). The skein relations satisfied by these expectation values are derived by conformal field-theory techniques. New hierarchies of invariant polynomials for knots in S 3 can be derived from these relations (at least) up to ten crossings. The N=3 Akutsu-Wadati polynomials are a special case with G=SO(3). The expectation value of the Wilson loops for a couple of simple unknotted circles is identified to the Weyl character.Work supported in part by U.S. National Science Foundation Grant PHY8706501.Work supported in party by Chinese National Science Foundation through Nankai University.
Keywords:81E40  81D15  22E65
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