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Modularity of open Gromov-Witten potentials of elliptic orbifolds. (English) Zbl 1347.81068
Summary: We study the modularity of the genus zero open Gromov-Witten potentials and its generating matrix factorizations for elliptic orbifolds. These objects constructed by Lagrangian Floer theory are a priori well-defined only around the large volume limit. It follows from modularity that they can be analytically continued over the global Kähler moduli space.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
57R58 Floer homology
57R18 Topology and geometry of orbifolds
14N10 Enumerative problems (combinatorial problems) in algebraic geometry
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
08B10 Congruence modularity, congruence distributivity
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