Chern-Simons perturbative series revisited

E. Lanina; A. Sleptsov; N. Tselousov

doi:10.1016/j.physletb.2021.136727

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arXiv · 2105.11565

Chern-Simons perturbative series revisited

E. Lanina·A. Sleptsov·N. Tselousov

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Abstract

A group-theoretical structure in a perturbative expansion of the Wilson loops in the 3d Chern-Simons theory with $SU(N)$ gauge group is studied in symmetric approach. A special basis in the center of the universal enveloping algebra $ZU(\mathfrak{sl}_N)$ is introduced. This basis allows one to present group factors in an arbitrary irreducible finite-dimensional representation. Developed methods have wide applications, the most straightforward and evident ones are mentioned. Namely, Vassiliev invariants of higher orders are computed, a conjecture about existence of new symmetries of the colored HOMFLY polynomials is stated, and the recently discovered tug-the-hook symmetry of the colored HOMFLY polynomial is proved.

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E. Lanina, A. Sleptsov, N. Tselousov. 2021-05-24. Chern-Simons perturbative series revisited. https://doi.org/10.1016/j.physletb.2021.136727

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