Quantum spectral curve operators for arbitrary base points can be derived by applying x-y and symplectic duality transformations to simpler spectral curves.
Topological Recursion for the extended Ooguri-Vafa partition function of colored HOMFLY-PT polynomials of torus knots
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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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Quantum Curves in the Context of Symplectic Duality
Quantum spectral curve operators for arbitrary base points can be derived by applying x-y and symplectic duality transformations to simpler spectral curves.