• Corpus ID: 248722004

Calabi-Yau/Landau-Ginzburg Correspondence for Weil-Peterson Metrics and $tt^*$ Structures

@inproceedings{Tang2022CalabiYauLandauGinzburgCF,
  title={Calabi-Yau/Landau-Ginzburg Correspondence for Weil-Peterson Metrics and \$tt^*\$ Structures},
  author={Xinxing Tang and Junrong Yan},
  year={2022}
}

• Xinxing Tang, Junrong Yan
• Published 11 May 2022
• Mathematics

. The goal of this paper is to establish the Calabi-Yau/Landau-Ginzburg (CY/LG) correspondence for the tt ∗ geometry structure, which is thought to hold all genus 0 information about B-models. More explicitly, given a non-degenerate homogeneous polynomial f ∈ C [ z 1 , . . . , z n ] of degree n , one can investigate the Landau-Ginzburg B-model, which concerns the deformation of singularities. Its zero set, on the other hand, defines a Calabi-Yau hypersurface X f in P n − 1 , whereas the Calabi-Yau B-model is concerned with the deformation of the complex structure on X f . Both LG B-model and CY B-model’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 B-model and the LG B-models.