从SYZ的矩阵分解的示例
Examples of Matrix Factorizations from SYZ
摘要：
我们发现矩阵分解对应于一个反对角线在${\mathbb C}P^1 \times {\mathbb C}P^1$，和圈纤维的加权投影线使用的想法Chan和梁的Strominger-Yau-Zaslow变换。对于泪滴orbifolds，我们应用这个想法找到两种类型的潜在的矩阵因式分解，通常的Hori-Vafa潜力或散装变形（orbi）的潜力。我们还证明了反对角线的直和及其位移，等价于Kapustin和Li从B模型计算中预测的${\mathbb C}P^1 \times {\mathbb C}P^1$中的中心环面纤维与完整性$(1,-1)$和$(-1,1)$的直和.
英文摘要：
We find matrix factorization corresponding to an anti-diagonal in ${\mathbb C}P^1 \times {\mathbb C}P^1$, 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 ${\mathbb C}P^1 \times {\mathbb C}P^1$, which was predicted by Kapustin and Li from B-model calculations.
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