SU(N) quantum Racah coefficients & non-torus links
Abstract
It is well-known that the SU(2) quantum Racah coefficients or the Wigner $6j$ 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.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2011
- DOI:
- 10.48550/arXiv.1107.3918
- arXiv:
- arXiv:1107.3918
- Bibcode:
- 2011arXiv1107.3918Z
- Keywords:
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- High Energy Physics - Theory;
- Mathematical Physics
- E-Print:
- 41 pages, 9 figures, Latex file, few typos corrected, added appendices of data in arXiv 1209.1346, added references,to appear in Nuclear Physics B