LG/CY Correspondence for Elliptic Orbifold Curves via Modularity

Abstract

We prove the Landau-Ginzburg/Calabi-Yau correspondence between the Gromov-Witten theory of each elliptic orbifold curve and its Fan-Jarvis-Ruan-Witten theory counterpart via modularity. We show that the correlation functions in these two enumerative theories are different representations of the same set of quasi-modular forms, expanded around different points on the upper-half plane. We relate these two representations by the Cayley transform.

v3: minor corrections

References in corpus (6)

• On Rationally Parametrized Modular Equations
• Gromov-Witten theory of elliptic orbifold P^1 and quasi-modular forms
• Landau-Ginzburg/Calabi-Yau Correspondence of all Genera for Elliptic Orbifold $p^1$
• Noncommutative homological mirror functor
• A proof of the Landau-Ginzburg/Calabi-Yau correspondence via the crepant transformation conjecture
• 6-dimensional FJRW theories of the simple-elliptic singularities

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• Higher Genus FJRW Invariants of a Fermat Cubic
• GKZ Hypergeometric Series for the Hesse Pencil, Chain Integrals and Orbifold Singularities
• Remarks on Symplectic Geometry