CalabiYau/LandauGinzburg Correspondence for WeilPeterson Metrics and $tt^*$ Structures
Abstract
The goal of this paper is to establish the CalabiYau/LandauGinzburg (CY/LG) correspondence for the $tt^*$ geometry structure, which is thought to hold all genus $0$ information about Bmodels. More explicitly, given a nondegenerate homogeneous polynomial $f\in\C[z_1,\ldots,z_n]$ of degree $n$, one can investigate the LandauGinzburg Bmodel, which concerns the deformation of singularities. Its zero set, on the other hand, defines a CalabiYau hypersurface $X_f$ in $\mathbb{P}^{n1}$, whereas the CalabiYau Bmodel is concerned with the deformation of the complex structure on $X_f$. Both LG Bmodel and CY Bmodel's genus 0 information can be captured by the $tt^*$ geometry structure. In this paper, we construct a map between the $tt^*$ structures on CY and LG's sides, and by a careful study of the period integrals, we build the isomorphism of $tt^*$ structures between the CY Bmodel and the LG Bmodels.
 Publication:

arXiv eprints
 Pub Date:
 May 2022
 arXiv:
 arXiv:2205.05791
 Bibcode:
 2022arXiv220505791T
 Keywords:

 Mathematical Physics;
 Mathematics  Algebraic Geometry;
 Mathematics  Differential Geometry
 EPrint:
 34 pages