The skein valued mirror of the topological vertex
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929642158424064 |
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| author | Ekholm, Tobias Longhi, Pietro Shende, Vivek |
| author_facet | Ekholm, Tobias Longhi, Pietro Shende, Vivek |
| contents | We count holomorphic curves in complex 3-space with boundaries on three special Lagrangian solid tori. The count is valued in the HOMFLYPT skein module of the union of the tori. Using 1-parameter families of curves at infinity, we derive three skein valued operator equations which must annihilate the count, and which dequantize to a mirror of the geometry. We show algebraically that the resulting equations determine the count uniquely, and that the result agrees with the topological vertex from topological string theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15454 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The skein valued mirror of the topological vertex Ekholm, Tobias Longhi, Pietro Shende, Vivek Symplectic Geometry High Energy Physics - Theory We count holomorphic curves in complex 3-space with boundaries on three special Lagrangian solid tori. The count is valued in the HOMFLYPT skein module of the union of the tori. Using 1-parameter families of curves at infinity, we derive three skein valued operator equations which must annihilate the count, and which dequantize to a mirror of the geometry. We show algebraically that the resulting equations determine the count uniquely, and that the result agrees with the topological vertex from topological string theory. |
| title | The skein valued mirror of the topological vertex |
| topic | Symplectic Geometry High Energy Physics - Theory |
| url | https://arxiv.org/abs/2412.15454 |