Modularity of Open Gromov-Witten Potentials of Elliptic Orbifolds

TL;DR

This paper investigates the modular properties of genus zero open Gromov-Witten potentials and their matrix factorizations for elliptic orbifolds, showing they can be analytically continued across the entire Kähler moduli space.

Contribution

It demonstrates the modularity of these potentials and matrix factorizations, enabling their extension beyond the large volume limit in elliptic orbifolds.

Findings

Modularity allows analytic continuation over the global Kähler moduli space.

Open Gromov-Witten potentials are well-defined near the large volume limit.

Matrix factorizations exhibit similar modular properties.

Abstract

We study the modularity of the genus zero open Gromov-Witten potentials and its generating matrix factorizations for elliptic orbifolds. These objects constructed by Lagrangian Floer theory are a priori well-defined only around the large volume limit. It follows from modularity that they can be analytically continued over the global K\"ahler moduli space.