Quantum algebraic approach to refined topological vertex
Quantum algebraic approach to refined topological vertex
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DOI：
10.1007/jhep03(2012)041
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发表时间：
2011-12
影响因子：
5.4
通讯作者：
H. Awata;B. Feigin;B. Feigin;B. Feigin;J. Shiraishi
中科院分区：
文献类型：
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作者：
H. Awata;B. Feigin;B. Feigin;B. Feigin;J. Shiraishi
我们建立了Iqbal-Kozcaz-Vafa的精化拓扑顶点与Miki引入的W 1+∞ 型量子代数的某种表示论之间的等价关系。我们的构造涉及与玻色 Fock 模块三元组相关的三价交织算子 Φ 和 Φ*。与拓扑顶点类似，每个交织算子都附加一个向量 ε 的三元组，满足 Calabi-Yau 和平滑条件。结果表明，Φ 和 Φ* 的某些矩阵元素给出了 Iqbal-Kozcaz-Vafa 的细化拓扑顶点 C λμν (t, q)。通过另一种基的选择，我们恢复了 Awata-Kanno 的精化拓扑顶点 C λμ ν (q, t)。当我们考虑 Φ 和 Φ* 的任何组合时，粘合因子会正确显示。附加到 Fock 空间的谱参数起着 Kähler 参数的作用。
We establish the equivalence between the refined topological vertex of Iqbal-Kozcaz-Vafa and a certain representation theory of the quantum algebra of type W 1+∞ introduced by Miki. Our construction involves trivalent intertwining operators Φ and Φ* associated with triples of the bosonic Fock modules. Resembling the topological vertex, a triple of vectors∈is attached to each intertwining operator, which satisfy the Calabi-Yau and smoothness conditions. It is shown that certain matrix elements of Φ and Φ* give the refined topological vertex C λμν (t, q) of Iqbal-Kozcaz-Vafa. With another choice of basis, we recover the refined topological vertex C λμ ν (q, t) of Awata-Kanno. The gluing factors appears correctly when we consider any compositions of Φ and Φ*. The spectral parameters attached to Fock spaces play the role of the Kähler parameters.