Counting surfaces on Calabi-Yau 4-folds II: $\mathrm{DT}$-$\mathrm{PT}_0$ correspondence
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929239040720896 |
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| author | Bae, Younghan Kool, Martijn Park, Hyeonjun |
| author_facet | Bae, Younghan Kool, Martijn Park, Hyeonjun |
| contents | This is the second part in a series of papers on counting surfaces on Calabi-Yau 4-folds. In this paper, we introduce $K$-theoretic $\mathrm{DT}, \mathrm{PT}_0, \mathrm{PT}_1$ invariants and conjecture a $\mathrm{DT}$-$\mathrm{PT}_0$ correspondence. For certain tautological insertions, we derive Lefschetz principles in both the compact and toric case allowing reductions to 3-dimensional $\mathrm{DT}, \mathrm{PT}$ invariants. We also develop a topological vertex and conjecture a $\mathrm{DT}$-$\mathrm{PT}_0$ vertex correspondence. These methods enable us to verify our conjectures in several examples. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_06526 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Counting surfaces on Calabi-Yau 4-folds II: $\mathrm{DT}$-$\mathrm{PT}_0$ correspondence Bae, Younghan Kool, Martijn Park, Hyeonjun Algebraic Geometry High Energy Physics - Theory 14N35 (Primary) 14D20, 14J35, 14J60, 14M25, 14N10 (Secondary) This is the second part in a series of papers on counting surfaces on Calabi-Yau 4-folds. In this paper, we introduce $K$-theoretic $\mathrm{DT}, \mathrm{PT}_0, \mathrm{PT}_1$ invariants and conjecture a $\mathrm{DT}$-$\mathrm{PT}_0$ correspondence. For certain tautological insertions, we derive Lefschetz principles in both the compact and toric case allowing reductions to 3-dimensional $\mathrm{DT}, \mathrm{PT}$ invariants. We also develop a topological vertex and conjecture a $\mathrm{DT}$-$\mathrm{PT}_0$ vertex correspondence. These methods enable us to verify our conjectures in several examples. |
| title | Counting surfaces on Calabi-Yau 4-folds II: $\mathrm{DT}$-$\mathrm{PT}_0$ correspondence |
| topic | Algebraic Geometry High Energy Physics - Theory 14N35 (Primary) 14D20, 14J35, 14J60, 14M25, 14N10 (Secondary) |
| url | https://arxiv.org/abs/2402.06526 |