{
  "abstract": "We study tree-level completions of four-dimensional $\\mathcal N=4$ Yang--Mills theory coupled to $\\mathcal N=4$ supergravity. Six-point factorization and supersymmetry Ward identities, supplemented by a peculiar-parity restriction on scalar contact terms, impose nonlinear relations between the single- and double-trace Wilson coefficients, $a_{k,q}$ and $b_{k,q}$, of the four-gluon amplitude. The simplest relation, $κ^2a_{0,0}=0$, excludes the single-trace $F^4$ interaction at nonzero gravitational coupling, despite its compatibility with four-point supersymmetry. On this gravitational branch, five double-trace parameters determine all coefficients through $a_{7,q}$ and $b_{8,q}$, which are reproduced by a common exponential generating form. Both the heterotic string and a family of infinite-spin-tower (IST) amplitudes realize this structure. Combining these relations with dispersion relations and partial-wave positivity in $SO(N)$ color channels yields a narrow numerical band closely bounded by the heterotic and simplest IST amplitudes. A spin-dependent mass gap excludes the IST spectrum and further localizes the region near the heterotic trajectory. An analytic unitarity analysis of the simplest IST gives $N\\leq48$ and $g^2/(κ^2 m^2)\\leq4$, matching the upper limits of the heterotic amplitude, where $m$ is the mass of the first massive level. Along the heterotic trajectory, the numerical bounds also sharply constrain the gauge-to-gravity coupling ratio at $N=48$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12318",
  "author_total": 3,
  "authors": [
    {
      "name": "Li-Yuan Chiang"
    },
    {
      "name": "Yu-tin Huang"
    },
    {
      "name": "He-Chen Weng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1f3cck26sg6fz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12318",
  "fulltext_url": null,
  "id": "1f3cck26sg6fz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12318",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7221189911",
  "pdf_url": "https://arxiv.org/pdf/2610.12318",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1f3cck26sg6fz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:54Z",
      "native_id": "2610.12318",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12318"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Cornering the Heterotic String",
  "title_text": "Cornering the Heterotic String",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:54Z",
  "url": "https://research.draconitic.com/paper/1f3cck26sg6fz",
  "venue": "arXiv",
  "versions": []
}