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arXiv · 2412.06527

Higher genus Gromov-Witten theory of one-parameter Calabi-Yau threefolds II: Feynman rule and anomaly equations

Patrick Lei
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Abstract

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.

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Patrick Lei. 2024-12-09. Higher genus Gromov-Witten theory of one-parameter Calabi-Yau threefolds II: Feynman rule and anomaly equations. https://arxiv.org/abs/2412.06527

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