image quantum Racah coefficients and non-torus links Original Research Article

It is well known that the image quantum Racah coefficients or the Wigner 6j symbols have a closed form expression which enables the evaluation of any knot or link polynomials in image Chern–Simons field theory. Using isotopy equivalence of image Chern–Simons functional integrals over three-balls with one or more image boundaries with punctures, we obtain identities to be satisfied by the image quantum Racah coefficients. This enables evaluation of the coefficients for a class of image 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.