Modularity of the open topological strings from topological recursion
ABSTRACT
The genus 0 open topological string amplitude for local P1×P1 can be computed from the Seiberg-Witten curve for 5d SU(2) theory. It can be related to the Abel-Jacobi map of an elliptic curve. Via topological recursion, it was proved that the higher genus open topological string amplitudes are quasi-meromorphic Jacobi forms. The goal of this talk is to first argue for the modular property from topological recursion, and then show some calculation results for local P1×P1 or local P2.