论文标题
Orbifold开/封闭的对应关系和镜像对称性
Orbifold Open/Closed Correspondence and Mirror Symmetry
论文作者
论文摘要
我们继续Mayr和Lerche-Mayr提出的开放/封闭对应关系的数学发展。给定在旋转的calabi-yau 3- orbifold $ \ mathcal {x} $的开放几何形状相对于框架的aganagic-vafa oftrane brane $（\ mathcal {l}，f）$，我们构建了一个toric calabi-yau 4- orbifold $ \ widetielde gromov-witten不变式与$（\ Mathcal {x}，\ Mathcal {l}，f），f）$的磁盘不变，在平滑情况下概括了作者的先前工作。然后，我们将对应关系升级到生成函数的级别，并证明$（\ Mathcal {x}，\ Mathcal {l}，f），f）$可以从Equivariant $ j $ -function $ j $ function中恢复$（\ Mathcal {x}}，\ Mathcal {l} $。我们进一步建立了$（\ Mathcal {x}，\ Mathcal {l}，f），f）$ $ i $ i $ function的$（Mathcal {x}，\ Mathcal {l}，f）的B模型对应关系，$ \ \ \ widetilde {\ mathcal {x {x}} $ copplience comport and Mirorry and contectors and symerryy insections coptry in and somenty，
We continue the mathematical development of the open/closed correspondence proposed by Mayr and Lerche-Mayr. Given an open geometry on a toric Calabi-Yau 3-orbifold $\mathcal{X}$ relative to a framed Aganagic-Vafa outer brane $(\mathcal{L},f)$, we construct a toric Calabi-Yau 4-orbifold $\widetilde{\mathcal{X}}$ and identify its genus-zero Gromov-Witten invariants with the disk invariants of $(\mathcal{X},\mathcal{L},f)$, generalizing prior work of the authors in the smooth case. We then upgrade the correspondence to the level of generating functions, and prove that the disk function of $(\mathcal{X},\mathcal{L},f)$ can be recovered from the equivariant $J$-function of $\widetilde{\mathcal{X}}$. We further establish a B-model correspondence that retrieves the B-model disk function of $(\mathcal{X},\mathcal{L},f)$ from the equivariant $I$-function of $\widetilde{\mathcal{X}}$, and show that the correspondences are compatible with mirror symmetry in both the open and closed sectors.
