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F-theory on K3 surfaces and orthogonal modular forms

  • Kazuhiro Sakai
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Abstract

We identify the precise F-theory backgrounds dual to the heterotic string theory compactified on T2 with general Wilson lines turned on for one of the two E8's. The elliptic curve describing the backgrounds is expressed in terms of orthogonal modular forms and is determined so that it admits a nontrivial scaling limit yielding a rational elliptic surface. We confirm that the curve reduces to the Seiberg-Witten curve for the E-string theory in this limit. We conjecture that our result gives an explicit inverse period map for algebraic K3 surfaces polarized by the U⊕ E8(−1) lattice.

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Cite

BibTeXRIS
BibTeX
@misc{sakai2026ftheory,
  title = {{F-theory on K3 surfaces and orthogonal modular forms}},
  author = {Kazuhiro Sakai},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10669},
  eprint = {2609.10669},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10669},
}
RIS
TY  - UNPB
TI  - F-theory on K3 surfaces and orthogonal modular forms
AU  - Kazuhiro Sakai
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.10669
UR  - https://arxiv.org/abs/2609.10669
AB  - We identify the precise F-theory backgrounds dual to the heterotic string theory compactified on T^2 with general Wilson lines turned on for one of the two E_8's. The elliptic curve describing the backgrounds is expressed in terms of orthogonal modular forms and is determined so that it admits a nontrivial scaling limit yielding a rational elliptic surface. We confirm that the curve reduces to the Seiberg-Witten curve for the E-string theory in this limit. We conjecture that our result gives an explicit inverse period map for algebraic K3 surfaces polarized by the U⊕ E_8(−1) lattice.
ER  -