Topological Fukaya category and mirror symmetry for toric Calabi-Yau 3-orbifolds
Qingyuan Bai, Bohan Fang
TL;DR
This paper establishes a homological mirror symmetry equivalence between the Fukaya-type A-model and the matrix factorization B-model for toric Calabi-Yau 3-orbifolds, extending previous results to orbifold cases.
Contribution
It extends homological mirror symmetry to include toric Calabi-Yau 3-orbifolds, connecting topological Fukaya categories with matrix factorizations in the orbifold setting.
Findings
Proves homological mirror symmetry for toric Calabi-Yau 3-orbifolds.
Defines a topological Fukaya-type category on the mirror curve.
Establishes equivalence with matrix factorization category for the orbifold.
Abstract
We prove a version of homological mirror symmetry statement for toric Calabi-Yau -orbifolds, thus extending arXiv:1604.06448 to the case of orbifolds under the mirror symmetry setting considered in arXiv:1604.07123. The B-model is the matrix factorization category for the toric Calabi-Yau -orbifold with a superpotential; while the A-model is a topologically defined Fukaya-type category on its mirror curve.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons