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

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.

49 pages. Fixed typos and mistakes, added formula for genus one GW potentials