POLYNOMIALS FOR TORUS LINKS FROM CHERN-SIMONS GAUGE-THEORIES

Invariant polynomials for torus links are obtained in the framework of the Chern-Simons topological gauge theory. The polynomials are comput ed as vacuum expectation values on the three-sphere of Wilson line ope rators representing the Verlinde algebra of the corresponding rational conformal field theory. In the case of the SU(2) gauge theory our res ults provide explicit expressions for the Jones polynomial as well as for the polynomials associated to the N-state (N > 2) vertex models (A kutsu-Wadati polynomials). By means of the Chern-Simons coset construc tion, the minimal unitary models are analyzed, showing that the corres ponding link invariants factorize into two SU(2) polynomials. A method to obtain skein rules from the Chern-Simons knot operators is develop ed. This procedure yields the eigenvalues of the braiding matrix of th e corresponding conformal field theory.