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} }
. 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…
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Constructing the LG/CY isomorphism between $tt^*$ geometries
- Mathematics
- 2022
A bstract . For a nondegenerate homogeneous polynomial f ∈ C [ z 0 ,. .., 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 ∗…
References
SHOWING 1-10 OF 30 REFERENCES
N=2 LANDAU-GINZBURG VS. CALABI-YAU σ-MODELS: NON-PERTURBATIVE ASPECTS
- Mathematics
- 1991
We discuss some nonperturbative aspects of the correspondence between N=2 Landau-Ginzburg orbifolds and Calabi-Yau σ-models. We suggest that the correct framework is Deligne’s theory of mixed Hodge…
Landau-Ginzburg/Calabi-Yau correspondence, global mirror symmetry and Orlov equivalence
- Mathematics
- 2012
We show that the Gromov-Witten theory of Calabi-Yau hypersurfaces matches, in genus zero and after an analytic continuation, the quantum singularity theory (FJRW theory) recently introduced by Fan,…
tt* geometry, Frobenius manifolds, their connections, and the construction for singularities
- Mathematics
- 2002
The base space of a semiuniversal unfolding of a hypersurface singularity carries a rich geometry. By work of K. Saito and M. Saito is can be equipped with the structure of a Frobenius manifold. By…
WITTEN DEFORMATION FOR NONCOMPACT MANIFOLDS WITH BOUNDED GEOMETRY
- MathematicsJournal of the Institute of Mathematics of Jussieu
- 2021
Motivated by the Landau–Ginzburg model, we study the Witten deformation on a noncompact manifold with bounded geometry, together with some tameness condition on the growth of the Morse function f…
Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes
- Mathematics
- 1994
We develop techniques to compute higher loop string amplitudes for twistedN=2 theories withĉ=3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in…
Primitive forms via polyvector fields
- Mathematics
- 2013
We develop a complex differential geometric approach to the theory of higher residues and primitive forms from the viewpoint of Kodaira-Spencer gauge theory, unifying the semi-infinite period maps…