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Conifold Gap for the Quintic Threefold
Abstract
We prove the all-genus conifold gap conjecture for the Gromov--Witten (GW) theories of the quintic threefold, other smooth Fermat Calabi--Yau threefold hypersurfaces, and local ℙ2, as well as for the FJRW theories associated with these hypersurfaces. Our proof uses Mixed Spin P-field (MSP) theory and analogous master-space constructions. The central object is the \emph{cone-vertex theory}. We express this theory as a translation of the point CohFT via a formal Laplace transform and prove a universal conifold gap theorem for the resulting translated theories. The master-space construction then transfers the gap from the cone-vertex theory to the GW and FJRW theories.
Related
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BibTeX
@misc{chang2026conifold,
title = {{Conifold Gap for the Quintic Threefold}},
author = {Huai-Liang Chang and Shuai Guo and Lei You and Huaigong Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13921},
eprint = {2609.13921},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13921},
}
RIS
TY - UNPB
TI - Conifold Gap for the Quintic Threefold
AU - Huai-Liang Chang
AU - Shuai Guo
AU - Lei You
AU - Huaigong Zhang
PY - 2026
DA - 2026/09/12
PB - arXiv
DO - 10.48550/arxiv.2609.13921
UR - https://arxiv.org/abs/2609.13921
AB - We prove the all-genus conifold gap conjecture for the Gromov--Witten (GW) theories of the quintic threefold, other smooth Fermat Calabi--Yau threefold hypersurfaces, and local ℙ^2, as well as for the FJRW theories associated with these hypersurfaces. Our proof uses Mixed Spin P-field (MSP) theory and analogous master-space constructions. The central object is the \emph{cone-vertex theory}. We express this theory as a translation of the point CohFT via a formal Laplace transform and prove a universal conifold gap theorem for the resulting translated theories. The master-space construction then transfers the gap from the cone-vertex theory to the GW and FJRW theories.
ER -