Quasimap SYZ for toric Calabi-Yau manifolds
Kwokwai Chan
TL;DR
This paper develops a new approach to the SYZ mirror construction for toric Calabi-Yau manifolds using quasimap Floer theory, confirming the mirror matches the physical predictions.
Contribution
It introduces quasimap Floer theory into the SYZ mirror construction, providing an alternative to traditional Lagrangian Floer theory for toric Calabi-Yau manifolds.
Findings
Mirror constructed via quasimap Floer theory matches the physical prediction.
Validates quasimap Floer theory as a tool in mirror symmetry.
Establishes equivalence with Fukaya-Oh-Ohta-Ono's approach.
Abstract
In this note, we study the SYZ mirror construction for a toric Calabi-Yau manifold using instanton corrections coming from Woodward's quasimap Floer theory instead of Fukaya-Oh-Ohta-Ono's Lagrangian Floer theory. We show that the resulting SYZ mirror coincides with the one written down via physical means (as expected).
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric and Algebraic Topology · Algebraic Geometry and Number Theory · Geometry and complex manifolds