Orbifold Open/Closed Correspondence and Mirror Symmetry
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| Format: | Preprint |
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2022
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| _version_ | 1866913930524229632 |
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| author | Liu, Chiu-Chu Melissa Yu, Song |
| author_facet | Liu, Chiu-Chu Melissa Yu, Song |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2210_11721 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Orbifold Open/Closed Correspondence and Mirror Symmetry Liu, Chiu-Chu Melissa Yu, Song Algebraic Geometry High Energy Physics - Theory 14N35 (Primary), 53D45, 14J33 (Secondary) 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. |
| title | Orbifold Open/Closed Correspondence and Mirror Symmetry |
| topic | Algebraic Geometry High Energy Physics - Theory 14N35 (Primary), 53D45, 14J33 (Secondary) |
| url | https://arxiv.org/abs/2210.11721 |