Hopf link invariants and integrable hierarchies
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 τ-function of the KP hierarchy. Furthermore, this Hopf generating function in the...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2025-01-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269324007287 |
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| Summary: | 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 τ-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 τ-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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| ISSN: | 0370-2693 |