Colored HOMFLY polynomials from Chern-Simons theory

Abstract

We elaborate the Chern-Simons field theoretic method to obtain colored HOMFLY invariants of knots and links. Using multiplicity-free quantum 6j-symbols for U_q(sl_N), we present explicit evaluations of the HOMFLY invariants colored by symmetric representations for a variety of knots, two-component links and three-component links.

40 pages, 23 figures, a Mathematica notebook linked on the right as an ancillary file; v2 typos corrected; v3 corrections in section 4.2 and cosmetic changes; v4 corrections in two-component links

References in corpus (5)

• HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations
• Character expansion for HOMFLY polynomials. III. All 3-Strand braids in the first symmetric representation
• 3d analogs of Argyres-Douglas theories and knot homologies
• Knot polynomials in the first non-symmetric representation
• On the formulae for the colored HOMFLY polynomials

Cited by in corpus (9)

• On colored HOMFLY polynomials for twist knots
• Colored HOMFLY polynomials that distinguish mutant knots
• Differential expansion and rectangular HOMFLY for the figure eight knot
• Differential expansion for link polynomials
• On R-matrix approaches to knot invariants
• Orthogonal Polynomials in Mathematical Physics
• Quantum Racah matrices up to level 3 and multicolored link invariants
• Torus knot polynomials and susy Wilson loops
• A simple proof of the strong integrality for full colored HOMFLYPT invariants