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arXiv · 1806.01146

A non-torus link from topological vertex

H. Awata·H. Kanno·A. Mironov·A. Morozov·An. Morozov
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Abstract

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 $L_{8n8}$. 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 $L_{8n8}$, which reduces to the Hopf link colored with two composite representations. Thus, this provides the first explicit example of non-torus link description through the topological vertex. It is not a real breakthrough, because $L_{8n8}$ is just a cable of the Hopf link, still, it can help to intensify the development of the formalism towards more interesting examples.

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H. Awata, H. Kanno, A. Mironov, A. Morozov, An. Morozov. 2018-06-04. A non-torus link from topological vertex. https://doi.org/10.1103/physrevd.98.046018

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