arXiv subjects

Patrick Lei

Publications and source records attributed to Patrick Lei.

3 recordsLinked to original sources

arXiv2024

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

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.

math.AG↗

arXiv2024

Higher-genus Gromov-Witten theory of one-parameter Calabi-Yau threefolds I: Polynomiality

We prove the finite generation conjecture of arXiv:hep-th/0406078 for the Gromov-Witten potentials of the Calabi-Yau hypersurfaces $Z_6 \subset \mathbb{P}(1,1,1,1,2)$, $Z_8 \subset \mathbb{P}(1,1,1,1,4)$, and $Z_{10} \subset \mathbb{P}(1,1,1,2,5)$ using the theory of MSP fields. In addition, a formula is given for the genus one Gromov-Witten potentials of these targets.

math.AG↗

arXiv2024

MSP theory for smooth Calabi-Yau threefolds in weighted $\mathbb{P}^4$

We develop the theory of $N$-mixed-spin-$P$ fields for Fermat-type hypersurfaces in $\mathbb{P}(1,1,1,1,2)$, $\mathbb{P}(1,1,1,1,4)$, and $\mathbb{P}(1,1,1,1,4)$, following the theory developed in arXiv:1809.08806 for the quintic threefold.

math.AG↗