The Topological String on the Quintic to Genus 83 and the Rank-Two D4-D2-D0 Indices
Abstract
We compute quintic Gopakumar-Vafa invariants for genera 2-83 and degrees up to 44 by integrating the holomorphic anomaly equations. Under rank-one modularity for the required Gieseker invariants and rank-two charge conjugation, a coupled system of boundary and surplus wall-crossing equations fixes the holomorphic ambiguities and 22 of the 36 polar rank-two D4-D2-D0 coefficients, without assuming any rank-two index. A computer-assisted extension of wall crossing supplies additional equations and the boundary datum needed to close the recursion through genus 83. With known low-genus input, the GV data are complete through degree 32 and yield PT and DT tables. Selected higher-genus wall-crossing invariants reach genus 216; 33 entries require additional hypotheses. Retrospectively selected extrapolations give conditional candidates at genera 84 and 85 and, with rank-two mock modularity, for the remaining polar coefficients.
Related
- Quintic Modification to Lifshitz Quasi-topological Black Holes
- Modularity of resurgent topological string
- The non-perturbative topological string: from resurgence to wall-crossing of DT invariants
- Defects in Topological Symmetric Orbifolds and their String Dual
- Topological String Blowup Equations via Stable Pairs
BibTeX
@misc{hecht2026topological,
title = {{The Topological String on the Quintic to Genus 83 and the Rank-Two D4-D2-D0 Indices}},
author = {Michael Hecht},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38473},
eprint = {2610.38473},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38473},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Topological String on the Quintic to Genus 83 and the Rank-Two D4-D2-D0 Indices
AU - Michael Hecht
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38473
UR - https://arxiv.org/abs/2610.38473
AB - We compute quintic Gopakumar-Vafa invariants for genera 2-83 and degrees up to 44 by integrating the holomorphic anomaly equations. Under rank-one modularity for the required Gieseker invariants and rank-two charge conjugation, a coupled system of boundary and surplus wall-crossing equations fixes the holomorphic ambiguities and 22 of the 36 polar rank-two D4-D2-D0 coefficients, without assuming any rank-two index. A computer-assisted extension of wall crossing supplies additional equations and the boundary datum needed to close the recursion through genus 83. With known low-genus input, the GV data are complete through degree 32 and yield PT and DT tables. Selected higher-genus wall-crossing invariants reach genus 216; 33 entries require additional hypotheses. Retrospectively selected extrapolations give conditional candidates at genera 84 and 85 and, with rank-two mock modularity, for the remaining polar coefficients.
ER -