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arXiv · 2010.11021

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

Petr Dunin-Barkowski·Maxim Kazarian·Aleksandr Popolitov·Sergey Shadrin·Alexey Sleptsov
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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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BibTeXRIS

Petr Dunin-Barkowski, Maxim Kazarian, Aleksandr Popolitov, Sergey Shadrin, Alexey Sleptsov. 2020-10-21. Topological Recursion for the extended Ooguri-Vafa partition function of colored HOMFLY-PT polynomials of torus knots. https://doi.org/10.4310/atmp.2022.v26.n4.a1

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