非平面拓扑三点形式
Non Planar Topological 3-Vertex Formalism
摘要：
利用复曲线在复射影平面$\bf{P }^{2}$上的嵌入，我们建立了局部Calabi-Yau三重$X^{(m,-m,0) }=\mathcal{O}(m)\oplus \mathcal{O}(-m)\to E^{(t,\infty)}$族上拓扑弦的\emph{non planar}拓扑三顶点形式.基$E^{(t,\infty)}$代表具有Kahler参数$t$的退化椭圆曲线;但是大的复杂结构$μ$ ;即$| μ| \longrightarrow \infty $。我们也给出了关于$X^{(m,-m,0)}$上A模型拓扑弦振幅的第一个结果。研究了退化椭圆曲线$ E^{(t,\infty)}$和$X^{(m,-m,0)}$族的二维$U(1) $规范$\mathcal{N}=2$超对称σ模型，明确地揭示了D项和F项的作用.
英文摘要：
Using embedding of complex curves in the complex projective plane $\bf{P }^{2}$, we develop a \emph{non planar} topological 3-vertex formalism for topological strings on the family of local Calabi-Yau threefolds $X^{(m,-m,0) }=\mathcal{O}(m)\oplus \mathcal{O}(-m)\to E^{(t,\infty)}$. The base $E^{(t,\infty)}$ stands for the degenerate elliptic curve with Kahler parameter $t$; but a large complex structure $μ$; i.e $| μ| \longrightarrow \infty $. We also give first results regarding A-model topological string amplitudes on $X^{(m,-m,0)}$. The 2D $U(1) $ gauged $\mathcal{N}=2$ supersymmetric sigma models of the degenerate elliptic curve $ E^{(t,\infty)}$ as well as for the family $X^{(m,-m,0)}$ are studied and the role of D- and F-terms is explicitly exhibited.
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