\(SU(N)\) quantum Racah coefficients and non-torus links

DOI10.1016/J.NUCLPHYSB.2012.12.020zbMATH Open1262.81168arXiv1107.3918OpenAlexW2749870112MaRDI QIDQ1950555

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Publication date: 13 May 2013

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Abstract: It is well-known that the SU(2) quantum Racah coefficients or the Wigner

6 j

symbols have a closed form expression which enables the evaluation of any knot or link polynomials in SU(2) Chern-Simons field theory. Using isotopy equivalence of SU(N) Chern-Simons functional integrals over three balls with one or more

S^{2}

boundaries with punctures, we obtain identities to be satisfied by the SU(N) quantum Racah coefficients. This enables evaluation of the coefficients for a class of SU(N) representations. Using these coefficients, we can compute the polynomials for some non-torus knots and two-component links. These results are useful for verifying conjectures in topological string theory.

Full work available at URL: https://arxiv.org/abs/1107.3918

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