论文标题
在$ tt^*$几何形状之间构建LG/CY同构
Constructing the LG/CY isomorphism between $tt^*$ geometries
论文作者
论文摘要
For a nondegenerate homogeneous polynomial $f\in\mathbb{C}[z_0, \dots, z_{n+1}]$ with degree $n+2$, we can obtain a $tt^*$ structure from the Landau-Ginzburg model $(\C^{n+2}, f)$ and a (new) $tt^*$ structure on the Calabi-Yau由$ f $ in $ \ c p^{n+1} $的零基因座定义的高度表面。我们可以证明，Steenbrink考虑的大残留图在两个$ tt^*$结构之间产生了同构。我们还为非卡拉比YAU案例建立了信件，事实证明只能保留部分结构。作为一个应用程序，我们表明，在恢复变形空间上Landau-Ginzburg模型的$ TT^*$几何结构唯一地确定了Calabi-yau侧的$ tt^*$几何结构。这解释了物理文献中的民间传说结论。该结果基于我们的早期工作\ cite {fly}。
For a nondegenerate homogeneous polynomial $f\in\mathbb{C}[z_0, \dots, z_{n+1}]$ with degree $n+2$, we can obtain a $tt^*$ structure from the Landau-Ginzburg model $(\C^{n+2}, f)$ and a (new) $tt^*$ structure on the Calabi-Yau hypersurface defined by the zero locus of $f$ in $\C P^{n+1}$. We can prove that the big residue map considered by Steenbrink gives an isomorphism between the two $tt^*$ structures. We also build the correspondence for non-Calabi-Yau cases, and it turns out that only partial structure can be preserved. As an application, we show that the $tt^*$ geometry structure of Landau-Ginzburg model on relavant deformation space uniquely determines the $tt^*$ geometry structure on Calabi-Yau side. This explains the folklore conclusion in physical literature. This result is based on our early work \cite{FLY}.
