Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1992-10-22
Nucl.Phys. B398 (1993) 187-236
Physics
High Energy Physics
High Energy Physics - Theory
50 pages
Scientific paper
10.1016/0550-3213(93)90632-Y
Invariant polynomials for torus links are obtained in the framework of the Chern-Simons topological gauge theory. The polynomials are computed as vacuum expectation values on the three-sphere of Wilson line operators representing the Verlinde algebra of the corresponding rational conformal field theory. In the case of the $SU(2)$ gauge theory our results provide explicit expressions for the Jones polynomial as well as for the polynomials associated to the $N$-state ($N>2$) vertex models (Akutsu-Wadati polynomials). By means of the Chern-Simons coset construction, the minimal unitary models are analyzed, showing that the corresponding link invariants factorize into two $SU(2)$ polynomials. A method to obtain skein rules from the Chern-Simons knot operators is developed. This procedure yields the eigenvalues of the braiding matrix of the corresponding conformal field theory.
Isidro Jose M.
Labastida Jose M. F.
Ramallo Alfonso V.
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