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

TL;DR

This paper proves the finite generation conjecture for Gromov-Witten potentials of certain Calabi-Yau hypersurfaces, providing explicit formulas for genus one potentials, advancing understanding in higher-genus Gromov-Witten theory.

Contribution

It establishes the finite generation of Gromov-Witten potentials for specific Calabi-Yau threefolds using MSP fields and derives formulas for genus one potentials, a novel achievement in the field.

Findings

Finite generation of Gromov-Witten potentials proved for three Calabi-Yau hypersurfaces.

Explicit formula derived for genus one Gromov-Witten potentials.

Advances the understanding of higher-genus Gromov-Witten invariants.

Abstract

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.