Advances in Theoretical and Mathematical Physics

Volume 26 (2022)

Number 4

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

Pages: 793 – 833

DOI: https://dx.doi.org/10.4310/ATMP.2022.v26.n4.a1

Authors

Petr Dunin-Barkowski (Faculty of Mathematics, National Research University Higher School of Economics, Moscow, Russia; HSE–Skoltech, Moscow, Russia; and NRC “Kurchatov Institute”, Moscow, Russia)

Maxim Kazarian (International Laboratory of Cluster Geometry, Faculty of Mathematics, National Research University Higher School of Economics, Moscow, Russia; and Center for Advanced Studies, Skoltech, Moscow, Russia)

Aleksandr Popolitov (Institute for Information Transmission Problems, Moscow, Russia; NRC “Kurchatov Institute”, Moscow, Russia; and Moscow Institute of Physics and Technology, Dolgoprudny, Russia)

Sergey Shadrin (Korteweg-de Vries Institute for Mathematics, University of Amsterdam, The Netherlands)

Alexey Sleptsov (NRC “Kurchatov Institute”, Moscow, Russia; Institute for Information Transmission Problems, Moscow, Russia; and Moscow Institute of Physics and Technology, Dolgoprudny, Russia)

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–Mariño 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).

Published 22 February 2023