Towards effective topological field theory for knots

  title={Towards effective topological field theory for knots},
  author={Andrei Mironov and A. Morozov},
  journal={Nuclear Physics},

Tabulating knot polynomials for arborescent knots

Arborescent knots are those which can be represented in terms of double fat graphs or equivalently as tree Feynman diagrams. This is the class of knots for which the present knowledge is sufficient

On rectangular HOMFLY for twist knots

As a new step in the study of rectangularly-colored knot polynomials, we reformulate the prescription [A. Morozov, arXiv:1606.06015v8] for twist knots in the double-column representations R = [rr] in

HOMFLY polynomials in representation [3, 1] for 3-strand braids

A bstractThis paper is a new step in the project of systematic description of colored knot polynomials started in [1]. In this paper, we managed to explicitly find the inclusive Racah matrix, i.e.

Factorization of differential expansion for antiparallel double-braid knots

A bstractContinuing the quest for exclusive Racah matrices, which are needed for evaluation of colored arborescent-knot polynomials in Chern-Simons theory, we suggest to extract them from a new kind

SU(2)/SL(2) knot invariants and KS monodromies

We review the Reshetikhin-Turaev approach to construction of non-compact knot invariants involving R-matrices associated with infinite-dimensional representations, primarily those made from Faddeev's

On universal knot polynomials

A bstractWe present a universal knot polynomials for 2- and 3-strand torus knots in adjoint representation, by universalization of appropriate Rosso-Jones formula. According to universality, these



Colored HOMFLY polynomials of knots presented as double fat diagrams

A bstractMany knots and links in S3 can be drawn as gluing of three manifolds with one or more four-punctured S2 boundaries. We call these knot diagrams as double fat graphs whose invariants involve

Eigenvalue hypothesis for Racah matrices and HOMFLY polynomials for 3-strand knots in any symmetric and antisymmetric representations

Character expansion expresses extended HOMFLY polynomials through traces of products of finite dimensional R- and Racah mixing matrices. We conjecture that the mixing matrices are expressed entirely

On colored HOMFLY polynomials for twist knots

Recent results of Gu and Jockers provide the lacking initial conditions for the evolution method in the case of the first nontrivially colored HOMFLY polynomials H[21] for the family of twist knots.

Colored HOMFLY polynomials for the pretzel knots and links

A bstractWith the help of the evolution method we calculate all HOMFLY polynomials in all symmetric representations [r] for a huge family of (generalized) pretzel links, which are made from g + 1 two

Character expansion for HOMFLY polynomials. II. Fundamental representation. Up to five strands in braid

A bstractCharacter expansion is introduced and explicitly constructed for the (noncolored) HOMFLY polynomials of the simplest knots. Expansion coefficients are not the knot invariants and can depend

Evolution method and"differential hierarchy"of colored knot polynomials

We consider braids with repeating patterns inside arbitrary knots which provides a multi-parametric family of knots, depending on the ”evolution” parameter, which controls the number of repetitions.

Cabling procedure for the colored HOMFLY polynomials

We discuss using the cabling procedure to calculate colored HOMFLY polynomials. We describe how it can be used and how the projectors and $\mathcal{R}$-matrices needed for this procedure can be