Year: 2026
Type: preprint
Abstract: We prove a version of topological recursion for the correlation differentials of colored HOMFLY-PT polynomials of torus knots on the corresponding augmentation curves, following the proposal of Gu, Jockers, Klemm, and Soroush. To this end, we explicitly construct the spectral curve from the so-called auxiliary curve of Brini, Eynard, and Mariño and prove that it coincides with the augmentation curve for every torus knot with coprime $(r,s)$. Finally, our version of topological recursion proves the higher-genus closed-string prediction of the Aganagic--Vafa conjecture for all torus knot augmentation curves.
Source: arXiv (Cornell University)
Authors: Hock, Alexander, Shadrin, Sergey
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222428752