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The Genus-One B-Model Calabi-Yau/Landau-Ginzburg Correspondence

  • Xinxing Tang
  • Junrong Yan
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Abstract

Let f:ℂn→ℂ be a homogeneous polynomial of degree n with an isolated critical point at the origin. The Calabi--Yau/Landau--Ginzburg correspondence predicts a close relation between invariants of the Landau--Ginzburg orbifold (ℂn/ℤn,f) and those of the associated Calabi--Yau hypersurface $ X_f=\{[z_1:\cdots:z_n]\in\mathbb P^{n-1}:f(z_1,\ldots,z_n)=0\}. $ In this paper, we establish this correspondence for the genus-one B-model by constructing the Landau--Ginzburg genus-one B-model invariant intrinsically from the f-twisted Laplacian on ℂn/ℤn and proving that it agrees with the corresponding BCOV invariant of Xf up to an additive constant depending only on the dimension.

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Cite

BibTeXRIS
BibTeX
@misc{tang2026genusone,
  title = {{The Genus-One B-Model Calabi-Yau/Landau-Ginzburg Correspondence}},
  author = {Xinxing Tang and Junrong Yan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33984},
  eprint = {2610.33984},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33984},
}
RIS
TY  - UNPB
TI  - The Genus-One B-Model Calabi-Yau/Landau-Ginzburg Correspondence
AU  - Xinxing Tang
AU  - Junrong Yan
PY  - 2026
DA  - 2026/10/25
PB  - arXiv
DO  - 10.48550/arxiv.2610.33984
UR  - https://arxiv.org/abs/2610.33984
AB  - Let f:ℂ^n→ℂ be a homogeneous polynomial of degree n with an isolated critical point at the origin. The Calabi--Yau/Landau--Ginzburg correspondence predicts a close relation between invariants of the Landau--Ginzburg orbifold (ℂ^n/ℤ_n,f) and those of the associated Calabi--Yau hypersurface $ X_f=\{[z_1:\cdots:z_n]\in\mathbb P^{n-1}:f(z_1,\ldots,z_n)=0\}. $ In this paper, we establish this correspondence for the genus-one B-model by constructing the Landau--Ginzburg genus-one B-model invariant intrinsically from the f-twisted Laplacian on ℂ^n/ℤ_n and proving that it agrees with the corresponding BCOV invariant of X_f up to an additive constant depending only on the dimension.
ER  -