Examples of Matrix Factorizations from SYZ

• Main Authors: Cheol-Hyun Cho, Hansol Hong, Sangwook Lee
• Format: Article
• Language: English
• Published: National Academy of Science of Ukraine 2012-08-01
• Series: Symmetry, Integrability and Geometry: Methods and Applications
• Subjects: matrix factorization; Fukaya category; mirror symmetry; Lagrangian Floer theory
• Online Access: http://dx.doi.org/10.3842/SIGMA.2012.053

We find matrix factorization corresponding to an anti-diagonal in CP^1×CP^1, and circle fibers in weighted projective lines using the idea of Chan and Leung of Strominger-Yau-Zaslow transformations. For the tear drop orbifolds, we apply this idea to find matrix factorizations for two types of potential, the usual Hori-Vafa potential or the bulk deformed (orbi)-potential. We also show that the direct sum of anti-diagonal with its shift, is equivalent to the direct sum of central torus fibers with holonomy (1,−1) and (−1,1) in the Fukaya category of CP^1×CP^1, which was predicted by Kapustin and Li from B-model calculations.