Calabi-Yau/Landau-Ginzburg Correspondence for $tt^*$ Structures
Time: 2022-09-21
Published By: Wenqiong Li
Speaker(s): Junrong Yan (Peking University)
Time: 14:00-15:00 September 27, 2022
Venue: Room 29, Quan Zhai, BICMR
Given a non-degenerate homogeneous polynomial $f\in\mathbb{C}[z_1,\ldots,z_n]$ of degree $n$, one can investigate the Landau-Ginzburg (LG) B-model, which concerns the deformation of singularities of $f$. Its zero set, on the other hand, defines a Calabi-Yau (CY) hypersurface $X_f$ in $\mathbb{P}^{n-1}$, whereas the Calabi-Yau B-model is concerned with the deformation of the complex structure on $X_f$. It is believed that the $tt^*$ geometry structure (a generalized version of variation of the Hodge structure) captures genus 0 information for both the LG B-model and the CY B-model. In recent joint work with Xinxing Tang, we constructed a map between the $tt^*$ structures on CY and LG's sides, and by a careful study of the period integrals on both sides, we built the isomorphism of $tt^*$ structures between the CY B-model and the LG B-models.
