Examples of Matrix Factorizations from SYZ
We find matrix factorization corresponding to an anti-diagonal in CP¹×CP¹, 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 potentia...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2012 |
| ISSN: | 1815-0659 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2012
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148404 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Examples of Matrix Factorizations from SYZ / Cheol-Hyun Cho, H. Hong, S. Lee // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 21 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We find matrix factorization corresponding to an anti-diagonal in CP¹×CP¹, 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 CP¹×CP¹, which was predicted by Kapustin and Li from B-model calculations.
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| ISSN: | 1815-0659 |