Examples of Matrix Factorizations from SYZ
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 potent...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
National Academy of Science of Ukraine
2012-08-01
|
| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.3842/SIGMA.2012.053 |
| Summary: | 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. |
|---|---|
| ISSN: | 1815-0659 |