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arXiv · 2210.11721

Orbifold Open/Closed Correspondence and Mirror Symmetry

Chiu-Chu Melissa Liu·Song Yu
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Abstract

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.

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Chiu-Chu Melissa Liu, Song Yu. 2022-10-21. Orbifold Open/Closed Correspondence and Mirror Symmetry. https://arxiv.org/abs/2210.11721

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