Jie Gu:Resurgent structure in topological strings

Abstract. Topological string theory has (spacetime) instanton sectors, which the resurgence theory predicts to be completely controlled by the perturbative free energy via Stokes transformations. Recent results also suggest the Stokes constants are related to BPS invariants/DT invariants. To make this picture complete, one needs to first solve the instanton amplitudes and then calculate the Stokes constants. We demonstrate that the first problem can be solved exactly and completely through a transseries extension of the BCOV holomorphic anomaly equations. We also make progress in the second problem. We focus on examples in local Calabi-Yau threefold and comment that similar results can be obtained for quintic as well.