On Asymptotics and Resurgent Structures of Enumerative Gromov-Witten Invariants

Understand

Making use of large-order techniques in asymptotics and resurgent analysis, this work addresses the growth of enumerative Gromov-Witten invariants---in their dependence upon genus and degree of the embedded curve---for several different threefold Calabi-Yau varieties.

• In particular, while the leading asymptotics of these invariants at large genus or at large degree is exponential, at combined large genus and degree it turns out to be factorial.
• This factorial growth has a resurgent nature, originating via mirror symmetry from the resurgent-transseries description of the B-model free energy.
• This implies the existence of nonperturbative sectors controlling the asymptotics of the Gromov-Witten invariants, which could themselves have an enumerative-geometry interpretation.