Pairings in Mirror Symmetry Between a Symplectic Manifold and a Landau-Ginzburg B-Model
- Authors
- Cho, Cheol-Hyun; Lee, Sangwook; Shin, Hyung-Seok
- Issue Date
- Apr-2020
- Publisher
- SPRINGER
- Citation
- COMMUNICATIONS IN MATHEMATICAL PHYSICS, v.375, no.1, pp.345 - 390
- Journal Title
- COMMUNICATIONS IN MATHEMATICAL PHYSICS
- Volume
- 375
- Number
- 1
- Start Page
- 345
- End Page
- 390
- URI
- http://scholarworks.bwise.kr/ssu/handle/2018.sw.ssu/39936
- DOI
- 10.1007/s00220-019-03611-4
- ISSN
- 0010-3616
- Abstract
- We find a relation between Lagrangian Floer pairing of a symplectic manifold and Kapustin-Li pairing of the mirror Landau-Ginzburg model under localized mirror functor. They are conformally equivalent with an interesting conformal factor (vol(Floer)/vol)(2), which can be described as a ratio of Lagrangian Floer volume class and classical volume class. For this purpose, we introduce B-invariant of Lagrangian Floer cohomology with values in Jacobian ring of the mirror potential function. And we prove what we call a multi-crescent Cardy identity under certain conditions, which is a generalized form of Cardy identity. As an application, we discuss the case of general toric manifold, and the relation to the work of Fukaya-Oh-Ohta-Ono and their Z-invariant. Also, we compute the conformal factor (vol(Floer)/vol)(2) for the elliptic curve quotient P-3,3,3(1), which gives a modular form.
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Collections - College of Natural Sciences > Department of Mathematics > 1. Journal Articles
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