Bulk-deformed potentials for toric Fano surfaces, wall-crossing and period

TL;DR

This paper develops an inductive algorithm to compute bulk-deformed potentials for toric Fano surfaces using wall-crossing and tropical-holomorphic correspondence, linking Gromov-Witten invariants with oscillatory integrals.

Contribution

It introduces a novel inductive method for calculating bulk-deformed potentials and proves a quantum period theorem connecting invariants with oscillatory integrals.

Findings

Successful computation of bulk-deformed potentials for toric Fano surfaces

Establishment of a correspondence between Gromov-Witten invariants and oscillatory integrals

Validation of the inductive algorithm through wall-crossing techniques

Abstract

We provide an inductive algorithm to compute the bulk-deformed potentials for toric Fano surfaces via wall-crossing techniques and a tropical-holomorphic correspondence theorem for holomorphic discs. As an application of the correspondence theorem, we also prove a big quantum period theorem for toric Fano surfaces which relates the log descendant Gromov-Witten invariants with the oscillatory integrals of the bulk-deformed potentials.