Higher genus Gromov-Witten theory of one-parameter Calabi-Yau threefolds II: Feynman rule and anomaly equations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917862991462400 |
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| author | Lei, Patrick |
| author_facet | Lei, Patrick |
| contents | We prove the Feynman rule conjectured by Bershadsky-Cecotti-Ooguri-Vafa arXiv:hep-th/9309140 and the anomaly equations conjectured by Yamaguchi-Yau arXiv:hep-th/0406078 for the Gromov-Witten theory of the Calabi-Yau threefolds $Z_6 \subset \mathbb{P}(1,1,1,1,2)$, $Z_8 \subset \mathbb{P}(1,1,1,1,4)$, and $Z_{10} \subset \mathbb{P}(1,1,1,2,5)$. These determine the generating series $F_g$ of genus $g$ Gromov-Witten invariants recursively from the lower-genus $F_{h<g}$ up to $3g-3$ unknown parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06527 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher genus Gromov-Witten theory of one-parameter Calabi-Yau threefolds II: Feynman rule and anomaly equations Lei, Patrick Algebraic Geometry We prove the Feynman rule conjectured by Bershadsky-Cecotti-Ooguri-Vafa arXiv:hep-th/9309140 and the anomaly equations conjectured by Yamaguchi-Yau arXiv:hep-th/0406078 for the Gromov-Witten theory of the Calabi-Yau threefolds $Z_6 \subset \mathbb{P}(1,1,1,1,2)$, $Z_8 \subset \mathbb{P}(1,1,1,1,4)$, and $Z_{10} \subset \mathbb{P}(1,1,1,2,5)$. These determine the generating series $F_g$ of genus $g$ Gromov-Witten invariants recursively from the lower-genus $F_{h<g}$ up to $3g-3$ unknown parameters. |
| title | Higher genus Gromov-Witten theory of one-parameter Calabi-Yau threefolds II: Feynman rule and anomaly equations |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2412.06527 |