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arXiv · 2410.14823

Hopf link invariants and integrable hierarchies

Chuanzhong Li·A. Mironov·A. Yu. Orlov
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Abstract

The goal of this note is to study integrable properties of a generating function of the HOMFLY-PT invariants of the Hopf link colored with different representations. We demonstrate that such a generating function is a $\tau$-function of the KP hierarchy. Furthermore, this Hopf generating function in the case of composite representations, which is a generating function of the 4-point functions in topological string (corresponding to the resolved conifold with branes on the four external legs), is a $\tau$-function of the universal character(UC) hierarchy put on the topological locus. We also briefly discuss a simple matrix model associated with the UC hierarchy.

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Chuanzhong Li, A. Mironov, A. Yu. Orlov. 2024-10-18. Hopf link invariants and integrable hierarchies. https://doi.org/10.1016/j.physletb.2024.139170

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