Nontorus link from topological vertex
Nontorus link from topological vertex
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DOI：
10.1103/physrevd.98.046018
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发表时间：
2018-06
影响因子：
5
通讯作者：
H. Awata;H. Kanno;A. Mironov;A. Morozov;A. Morozov
中科院分区：
文献类型：
--
作者：
H. Awata;H. Kanno;A. Mironov;A. Morozov;A. Morozov
最近提出的纽结多项式的缠结演算是密切相关的拓扑弦的考虑，可以帮助建立HOMFLY-PT不变量的拓扑顶点。我们在最简单的例子中讨论这种相互作用的霍普夫链接和链接$L_{8 n8}$。结果表明，在拓扑弦的四个外支上具有四种不同表示的解析锥状结构可以用四分量链L_{8 n8}$的特殊投影来描述，它可以简化为具有两种复合表示的Hopf链。因此，这提供了通过拓扑顶点的非环面链路描述的第一个显式示例。这不是一个真实的突破，因为$L_{8 n8}$只是Hopf链的一根索，但它仍然有助于加强形式主义向更有趣的例子的发展。
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.