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Polynomials for Torus Links from Chern-Simons Gauge Theories

J. M. Isidro·J. M. F. Labastida·A. V. Ramallo
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Abstract

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.

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J. M. Isidro, J. M. F. Labastida, A. V. Ramallo. 1992-10-22. Polynomials for Torus Links from Chern-Simons Gauge Theories. https://doi.org/10.1016/0550-3213(93)90632-y

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