论文标题
热带顶点
The tropological vertex
论文作者
论文摘要
拓扑顶点的理论最初是由Aganagic，klemm，mariño和vafa提出的，是计算开放的gromov-witten thifolds的开放式gromov-witten不变性。在本文中，我们将拓扑顶点放置在log calabi-yau流形的相对格罗莫夫不变的背景下，并描述如何通过胶合公式有效地计算这些不变性，以枚举热带曲线在奇异的整体仿射空间中。这种更丰富的环境使我们能够证明拓扑顶点具有某些热带对称性。这些对称性是通过量子曲线的作用来捕获的，该量子曲线是与热带顶点组的Lie代数，Pandharipande和Siebert的定量有关的。最后，我们证明了对称的代数如何导致对拓扑顶点和相关的Gromov-witten不变性的明确描述。
The theory of the topological vertex was originally proposed by Aganagic, Klemm, Mariño and Vafa as a means to calculate open Gromov-Witten invariants of toric Calabi-Yau threefolds. In this paper, we place the topological vertex within the context of relative Gromov-Witten invariants of log Calabi-Yau manifolds and describe how these invariants can be effectively computed via a gluing formula for the enumeration of tropical curves in a singular integral affine space. This richer context allows us to prove that the topological vertex possesses certain tropical symmetries. These symmetries are captured by the action of a quantum torus Lie algebra that is related to a quantisation of the Lie algebra of the tropical vertex group of Gross, Pandharipande and Siebert. Finally, we demonstrate how this algebra of symmetries leads to an explicit description of the topological vertex and related Gromov-Witten invariants.
