{
  "abstract": "We show that a three-body holonomy can select the conventional $SU(3)\\to SU(2)\\times U(1)$ breaking direction. Three particles are special in the present construction: after removal of the center-of-mass coordinate they are the minimal one-dimensional few-body system with a two-dimensional relative space, allowing a closed cycle around the triple-coincidence point once pairwise contacts are encoded by matching conditions. A cyclic three-state mass operator gives \\[ M^{[k]}=M_0+2Δ\\cos\\!\\left(\\frac{θ_3+2πk}{3}\\right),\\qquad k=0,1,2. \\] At $θ_3=0$ the spectrum splits as $3\\to2+1$, and the induced mass operator is proportional to the Cartan generator $T_8$. Its commutant is therefore $SU(2)\\times U(1)$. In a trinification-like embedding, distinct left- and right-sector holonomies leave the hypercharge combination which reproduces the Standard-Model hypercharges for the usual trinification matter assignment. The construction is a toy mechanism for selecting the breaking direction; additional dynamics are required for rank reduction and vacuum selection.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00235",
  "author_total": 1,
  "authors": [
    {
      "name": "Tadashi Yoshikawa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/csaa2yn13fmc6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00235",
  "fulltext_url": null,
  "id": "csaa2yn13fmc6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00235",
  "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/2610.00235",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/csaa2yn13fmc6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.00235",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00235"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "Three-Body Holonomy and $SU(3)\\to SU(2)\\times U(1)$ Symmetry Breaking",
  "title_text": "Three-Body Holonomy and SU(3)→ SU(2)× U(1) Symmetry Breaking",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:03Z",
  "url": "https://research.draconitic.com/paper/csaa2yn13fmc6",
  "venue": "arXiv",
  "versions": []
}