Nontorus link from topological vertex

The recently suggested tangle calculus for knot polynomials is intimately related to topological string considerations and can help to build the HOMFLY-PT invariants from the topological vertices. We discuss this interplay in the simplest example of the Hopf link and link L8n8. It turns out that the...

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Bibliographic Details
Published in:Physical review. D 2018-08, Vol.98 (4), Article 046018
Main Authors: Awata, Hidetoshi, Kanno, Hiroaki, Mironov, Andrei, Morozov, Alexei, Morozov, Andrey
Format: Article
Language:English
Subjects:
Polynomials
Representations
Toruses
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Summary:The recently suggested tangle calculus for knot polynomials is intimately related to topological string considerations and can help to build the HOMFLY-PT invariants from the topological vertices. We discuss this interplay in the simplest example of the Hopf link and link L8n8. It turns out that the resolved conifold with four different representations on the four external legs, on the topological string side, is described by a special projection of the four-component link L8n8, which reduces to the Hopf link colored with two composite representations. Thus, this provides the first explicit example of non-torus link description through topological vertex. It is not a real breakthrough, because L8n8 is just a cable of the Hopf link, still it can help to intensify the development of the formalism towards more interesting examples.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.98.046018