Conifold factorization in topological recursion and Gromov--Witten theory
Abstract
We prove a factorization theorem for ordinary topological recursion near a regular nodal degeneration of a spectral curve, allowing logarithmic spectral coordinates. The partition function for closed genera g≥2 factors into the partition function of the normalization, a universal Gaussian vacuum, and the exponential of a connected graph sum. This graph sum has strictly positive order in the vanishing period, and thus the factorization recovers the conifold gap, identifies the term of degree zero in the vanishing period with the free energy of the normalization, and gives finite graph formulas for the coefficients of positive powers of the period. At fixed genus, the regular series converges jointly in the period and the parameters along the nodal locus. The Gaussian neck tensors can be expressed in terms of relative Gromov--Witten invariants of a parametrized ℙ1. As examples, we use remodeling to obtain Gromov--Witten factorizations for local ℙ2 and local 𝔽0 in the conifold frame, with backgrounds ℂ3 and the resolved conifold, respectively. The analogous local 𝔽1 factorization has background 𝒪(1)⊕𝒪(−3) over ℙ1.
Related
- Two Recursions for the Seiberg-Witten Prepotential: Zamolodchikov's Recursion, the AGT Correspondence and Topological Recursion on the Seiberg-Witten Curve
- Gauss-Manin Connection in Disguise: Holomorphic Anomaly Equations and Higher Genus Real Gromov-Witten Invariants
- From Closed to Relative Higher-Genus Gromov-Witten Invariants via Resurgent Functions
- Mapping-space Gromov--Witten classes and the Fano variety of lines
- From wall structures to closed mirror symmetry. The case of Kℙ2: Renormalized periods over the positive real locus, closed Gromov-Witten invariants from wall functions, and tropical enumeration
BibTeX
@misc{chen2026conifold,
title = {{Conifold factorization in topological recursion and Gromov--Witten theory}},
author = {Juping Chen and Linji Chen and Bohan Fang and Zhengyu Zong},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01557},
eprint = {2610.01557},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01557},
}
RIS
TY - UNPB
TI - Conifold factorization in topological recursion and Gromov--Witten theory
AU - Juping Chen
AU - Linji Chen
AU - Bohan Fang
AU - Zhengyu Zong
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01557
UR - https://arxiv.org/abs/2610.01557
AB - We prove a factorization theorem for ordinary topological recursion near a regular nodal degeneration of a spectral curve, allowing logarithmic spectral coordinates. The partition function for closed genera g≥2 factors into the partition function of the normalization, a universal Gaussian vacuum, and the exponential of a connected graph sum. This graph sum has strictly positive order in the vanishing period, and thus the factorization recovers the conifold gap, identifies the term of degree zero in the vanishing period with the free energy of the normalization, and gives finite graph formulas for the coefficients of positive powers of the period. At fixed genus, the regular series converges jointly in the period and the parameters along the nodal locus. The Gaussian neck tensors can be expressed in terms of relative Gromov--Witten invariants of a parametrized ℙ^1. As examples, we use remodeling to obtain Gromov--Witten factorizations for local ℙ^2 and local 𝔽_0 in the conifold frame, with backgrounds ℂ^3 and the resolved conifold, respectively. The analogous local 𝔽_1 factorization has background 𝒪(1)⊕𝒪(−3) over ℙ^1.
ER -