Towards effective topological field theory for knots

A. Mironov, A. Morozov
2015 Nuclear Physics B  
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 $R\otimes R\otimes\bar R\longrightarrow \bar R$ and mixing
more » ... $ and mixing matrices in the sectors $R^{\otimes 3}\longrightarrow Q$. 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).
doi:10.1016/j.nuclphysb.2015.08.005 fatcat:65jlwtekyzgjfbrbdxoejew7ny