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PreprintCC BY 4.0arXiv

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

  • Murad Alim
  • Noah Tischler
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Abstract

Higher genus Gromov-Witten invariants of Calabi-Yau threefolds are encoded in a generating function which is an asymptotic series in a formal parameter λ. 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/λ$, 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.

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Cite

BibTeXRIS
BibTeX
@misc{alim2026from,
  title = {{From Closed to Relative Higher-Genus Gromov-Witten Invariants via Resurgent Functions}},
  author = {Murad Alim and Noah Tischler},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.09256},
  eprint = {2609.09256},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09256},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - From Closed to Relative Higher-Genus Gromov-Witten Invariants via Resurgent Functions
AU  - Murad Alim
AU  - Noah Tischler
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.09256
UR  - https://arxiv.org/abs/2609.09256
AB  - Higher genus Gromov-Witten invariants of Calabi-Yau threefolds are encoded in a generating function which is an asymptotic series in a formal parameter λ. 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/λ$, 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.
ER  -