{
  "abstract": "In heterotic string compactifications on toroidal orbifolds, the massless states at a twisted fixed point are constrained by the evenness of the sixteen-dimensional gauge lattice. We show that two massless left-chiral states in the same Standard-Model representation, built on the same constructing space-group element and distinct modulo the Weyl group of $SU(3)_c\\times SU(2)_L$, must satisfy $\\sqrt{R}+\\sqrt{R'}\\ge\\sqrt{2}$, where $R$ is the squared length of the part of a state's gauge momentum orthogonal to the Standard-Model Cartan directions. Without left-moving oscillator excitations this reads $R\\ge 1/2$. When $R<1$, $n$ such states, pairwise distinct in the same sense, carry the weights of the fundamental representation of a local $SU(n)$ commuting with the Standard Model, and $n\\le 1/(1-R)$. Since the representation fixes the projected length (at the canonical hypercharge normalisation, $6/5$ for the 10-like $Q$, $u^c$, $e^c$ and $4/5$ for the 5bar-like $d^c$ and lepton doublet), the bound becomes a condition on the sector: a repeated 10-like representation requires a massless budget of at least $17/20$, a repeated 5bar-like one at least $13/20$. In the complete massless spectra of 16,138 models from two orbifold catalogues the multiplicity ceiling is reached at four values of $R$. We exhibit an explicit model on $T^6/(Z_3\\times Z_6)$ whose budget clears the higher threshold and carries a repeated 10-like representation at the multiplicity the bound permits. For the Standard Model embedded through $SU(5)$ in one $E_8$ factor we show that, for that geometry and budget, exactly two inequivalent order-six shift classes admit such a doubling, and among the embeddings over them with the Standard Model intact we find none with three net generations of $Q$, $u^c$ and $e^c$ at once.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31873",
  "author_total": 1,
  "authors": [
    {
      "name": "Navid Ardakanian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d3x018v6ywdmm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31873",
  "fulltext_url": null,
  "id": "d3x018v6ywdmm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31873",
  "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-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.31873",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d3x018v6ywdmm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:15Z",
      "native_id": "2610.31873",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31873"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "A localisation bound for Standard-Model representations in heterotic orbifolds",
  "title_text": "A localisation bound for Standard-Model representations in heterotic orbifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:15Z",
  "url": "https://research.draconitic.com/paper/d3x018v6ywdmm",
  "venue": "arXiv",
  "versions": []
}