From Closed to Relative Higher-Genus Gromov-Witten Invariants via Resurgent Functions

RESUMO

Higher genus Gromov-Witten invariants of Calabi-Yau threefolds are encoded in a generating function which is an asymptotic series in a formal parameter $\lambda$. Using resurgence, analytic functions in this formal parameter were uncovered. In this paper we focus on the resolved conifold and study the enumerative meaning of the strong-coupling asymptotic expansion, in powers of $ 1/\lambda $, of the resurgent analytic functions. We show that this expansion contains both a closed curve-counting contribution in dual variables and a contribution governed by relative Gromov-Witten invariants, naturally interpreted in logarithmic geometry.