The Topological Open String Wavefunction

We show that, in local Calabi–Yau manifolds, the topological open string partition function transforms as a wavefunction under modular transformations. Our derivation is based on the topological recursion for matrix models, and it generalizes in a natural way the known result for the closed topological string sector. As an application, we derive results for vacuum expectation values of 1/2 BPS Wilson loops in ABJM theory at all genera in a strong coupling expansion, for various representations.