标题： 顶点算子，$\mathbb{C}^3$曲线与拓扑顶点 显示英文标题

标题： Vertex Operators, $\mathbb{C}^3$ Curve and Topological Vertex

摘要： 本文证明了拓扑顶点的 Kodaira-Spencer 理论是一个自由费米子理论的猜想。通过将$\mathbb{C}^3$曲线分为核区和渐近区，并利用玻色-费米对应关系，我们构造了一个通用的三腿相关函数，以算子方法重新表述了拓扑顶点。我们提出了一个相关函数恒等式的猜想，退化情况下该恒等式变为周\rq{}对于 Hopf 链的恒等式。 显示英文摘要

摘要： In this article, we prove the conjecture that Kodaira-Spencer theory for the topological vertex is a free fermion theory. By dividing the $\mathbb{C}^3$ curve into core and asymptotic regions and using Boson-Fermion correspondence, we construct a generic three-leg correlation function which reformulates the topological vertex in a vertex operator approach. We propose a conjecture of the correlation function identity which in a degenerate case becomes Zhou\rq{}s identity for a Hopf link.