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This article is cited in 6 scientific papers (total in 6 papers)
Examples of matrix factorizations from SYZ
Cheol-Hyun Cho, Hansol Hong, Sangwook Lee Department of Mathematics, Research Institute of Mathematics, Seoul National University, 1 Kwanak-ro, Kwanak-gu, Seoul, South Korea
Abstract:
We find matrix factorization corresponding to an anti-diagonal in $\mathbb CP^1 \times \mathbb CP^1$, 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 $\mathbb CP^1 \times \mathbb CP^1$, which was predicted by Kapustin and Li from B-model calculations.
Keywords:
matrix factorization, Fukaya category, mirror symmetry, Lagrangian Floer theory.
Received: May 15, 2012; in final form August 12, 2012; Published online August 16, 2012
Citation:
Cheol-Hyun Cho, Hansol Hong, Sangwook Lee, “Examples of matrix factorizations from SYZ”, SIGMA, 8 (2012), 053, 24 pp.
Linking options:
https://www.mathnet.ru/eng/sigma730 https://www.mathnet.ru/eng/sigma/v8/p53
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