Topological Recursion for the extended Ooguri-Vafa partition function of colored HOMFLY-PT polynomials of torus knots

Abstract

We prove that topological recursion applied to the spectral curve of colored HOMFLY-PT polynomials of torus knots reproduces the n-point functions of a particular partition function called the extended Ooguri-Vafa partition function. This generalizes and refines the results of Brini-Eynard-Marino and Borot-Eynard-Orantin. We also discuss how the statement of spectral curve topological recursion in this case fits into the program of Alexandrov-Chapuy-Eynard-Harnad of establishing the topological recursion for general weighted double Hurwitz numbers partition functions (a.k.a. KP tau-functions of hypergeometric type).

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Cited by in corpus (4)

• Topological recursion for Kadomtsev-Petviashvili tau functions of hypergeometric type
• Harer-Zagier formulas for knot matrix models
• Log topological recursion through the prism of $x-y$ swap
• Topological recursion, symplectic duality, and generalized fully simple maps