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Pairings in Mirror Symmetry Between a Symplectic Manifold and a Landau-Ginzburg B-Model
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- Authors
- Issue Date
- 2020-04
- Publisher
- Springer Verlag
- Citation
- Communications in Mathematical Physics, Vol.375 No.1, pp.345-390
- 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.
- ISSN
- 0010-3616
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