{
  "abstract": "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 $U\\oplus E_8(-1)$ lattice.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10669",
  "author_total": 1,
  "authors": [
    {
      "name": "Kazuhiro Sakai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cpacy5va44amn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10669",
  "fulltext_url": null,
  "id": "cpacy5va44amn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10669",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7212223795",
  "pdf_url": "https://arxiv.org/pdf/2609.10669",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cpacy5va44amn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:26Z",
      "native_id": "2609.10669",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10669"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "F-theory on K3 surfaces and orthogonal modular forms",
  "title_text": "F-theory on K3 surfaces and orthogonal modular forms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/cpacy5va44amn",
  "venue": "arXiv",
  "versions": []
}