Genus expansion of HOMFLY polynomials

Understand

In the planar limit of the 't Hooft expansion, the Wilson-loop average in 3d Chern-Simons theory (i.e.

• the HOMFLY polynomial) depends in a very simple way on representation (the Young diagram), so that the (knot-dependent) Ooguri-Vafa partition function becomes a trivial KP tau-function.
• We study higher genus corrections to this formula in the form of expansion in powers of z = q-q^{-1}.
• Expansion coefficients are expressed through the eigenvalues of the cut-and-join operators, i.e.