论文标题
Weil-Peterson指标和$ tt^*$结构的Calabi-Yau/Landau-Ginzburg通信
Calabi-Yau/Landau-Ginzburg Correspondence for Weil-Peterson Metrics and $tt^*$ Structures
论文作者
论文摘要
本文的目的是严格建立Calabi-yau/Landau-Ginzburg（CY/LG）的$ tt^*$几何结构 - 霍奇结构变化的广义版本。尽管众所周知，LG和CY的侧面的Hodge结构之间存在图，以保留Hodge过滤和双线性形式，但尚不清楚是否也保留了实际结构。在我们的论文中，我们对LG方面的两个时期积分进行了详细的分析。基于此分析，我们修改了Cecotti在LG方面提出的实际结构，并表明上述地图也保留在修改后的实际结构下。结果，我们为$ tt^*$结构建立了完整的CY/LG通信。
The aim of this paper is to rigorously establish the Calabi-Yau/Landau-Ginzburg (CY/LG) correspondence for the $tt^*$ geometry structure--a generalized version of variation of Hodge structures. Although it is well-known that there exists a map between Hodge structures on the LG and CY's sides that preserves the Hodge filtration and bilinear form, it remains unclear whether the real structures are also preserved. In our paper, we conduct a detailed analysis of two period integrals on the LG's side. Based on this analysis, we modify the real structure proposed by Cecotti on LG's side, and show that the aforementioned map is also preserved under the modified real structure. As a result, we establish full CY/LG correspondence for $tt^*$ structures.
