Genus Two Quasi-Siegel Modular Forms and Gromov-Witten Theory of Toric Calabi-Yau Threefolds

Abstract

We first develop theories of differential rings of quasi-Siegel modular and quasi-Siegel Jacobi forms for genus two. Then we apply them to the Eynard-Orantin topological recursion of certain local Calabi-Yau threefolds equipped with branes, whose mirror curves are genus two hyperelliptic curves. By the proof of the Remodeling Conjecture, we prove that the corresponding open- and closed- Gromov-Witten potentials are essentially quasi-Siegel Jacobi and quasi-Siegel modular forms for genus two, respectively.

minor revision. A shortened version to appear in Commun. Math. Phys

References in corpus (3)

• Remodeling the B-model
• The Satake sextic in elliptic fibrations on K3
• Open Gromov-Witten Theory of $K_{{\mathbb{P}}^2},K_{{\mathbb{P}}^1\times {\mathbb{P}}^1},K_{W\mathbb{P}[1,1,2]},K_{{\mathbb{F}}_1}$ and Jacobi Forms

Cited by in corpus (2)

• Canonical Differential Equations Beyond Genus One
• Probing Quantum Curves and Transitions in 5d SQFTs via Defects and Blowup Equations