We study the open refined topological string amplitudes using the refined topological vertex. We determine the refinement of holonomies necessary to describe the boundary conditions of open amplitudes (which in particular satisfy the required integrality properties). We also derive the refined holonomies using the refined Chern-Simons theory.

中文翻译：

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精细拓扑膜

我们使用细化拓扑顶点研究开放细化拓扑弦振幅。我们确定了描述开放振幅的边界条件（特别是满足所需的完整性属性）所需的完整度的细化。我们还使用精炼的陈-西蒙斯理论推导出精炼的全息法。