PreprintarXiv licencearXiv
Spectral Curves for Semisimple Conformal Frobenius Manifolds
Abstract
We construct connected spectral curves for semisimple conformal Frobenius manifolds with flat unit, using the periods of the second structure equation. Eynard-Orantin topological recursion on these curves reproduces the stable ancestor correlators of Givental-Teleman reconstruction. The spectral curves are defined on simply connected domains in the complex plane. We apply the construction to the quantum cohomology of ℙn for n≥2 at a point, obtaining explicit spectral curve data in terms of Hecke triangle groups and hypergeometric functions. Finally, for ℙ2 and ℙ3, we express the complete spectral curve data, including the bidifferentials, in classical modular and quasimodular forms.
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BibTeX
@misc{xiong2026spectral,
title = {{Spectral Curves for Semisimple Conformal Frobenius Manifolds}},
author = {Dingkang Xiong and Jian Zhou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24985},
eprint = {2610.24985},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24985},
}
RIS
TY - UNPB
TI - Spectral Curves for Semisimple Conformal Frobenius Manifolds
AU - Dingkang Xiong
AU - Jian Zhou
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.24985
UR - https://arxiv.org/abs/2610.24985
AB - We construct connected spectral curves for semisimple conformal Frobenius manifolds with flat unit, using the periods of the second structure equation. Eynard-Orantin topological recursion on these curves reproduces the stable ancestor correlators of Givental-Teleman reconstruction. The spectral curves are defined on simply connected domains in the complex plane. We apply the construction to the quantum cohomology of ℙ^n for n≥2 at a point, obtaining explicit spectral curve data in terms of Hecke triangle groups and hypergeometric functions. Finally, for ℙ^2 and ℙ^3, we express the complete spectral curve data, including the bidifferentials, in classical modular and quasimodular forms.
ER -