Towards effective topological field theory for knots

2015/06/12 by A. Mironov, A. Morozov · 3 citations
Physics and Astronomy · Mathematics · #hep-th #math.GT #math.QA

paper · pdf · doi:10.1016/j.nuclphysb.2015.08.005

published as Nucl.Phys. B899 (2015) 395-413 · 10 pages + table in Appendix

arxiv created 2015/06/12 · arxiv updated 2015/08/31

Abstract

Construction of (colored) knot polynomials for double-fat graphs is further generalized to the case when "fingers" and "propagators" are substituting R-matrices in arbitrary closed braids with m-strands. Original version of arXiv:1504.00371 corresponds to the case m=2, and our generalizations sheds additional light on the structure of those mysterious formulas. Explicit expressions are now combined from Racah matrices of the type R⊗ R⊗ R\longrightarrow R and mixing matrices in the sectors R^{⊗ 3}\longrightarrow Q. Further extension is provided by composition rules, allowing to glue two blocks, connected by an m-strand braid (they generalize the product formula for ordinary composite knots with m=1).

Citations

• Colored HOMFLY polynomials of knots presented as double fat diagrams

Cited by

• Colored knot polynomials. HOMFLY in representation [2,1]
• HOMFLY polynomials in representation [3,1] for 3-strand braids
• Quantum Racah matrices and 3-strand braids in representation [3,3]