SU(N) quantum Racah coefficients & non-torus links

Details SU(N) quantum Racah coefficients & non-torus links SU(N) quantum Racah coefficients & non-torus links

2011-07-20

arxiv.org/abs/1107.3918v4

Physics

High Energy Physics

High Energy Physics - Theory

1+32 pages, 9 figures, Latex file, few typos corrected

Scientific paper

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.

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