{
  "abstract": "We investigate the geometry of the Fermion mixing matrix in the Standard Model. The principal structure studied is the CKM matrix, $V$, viewed as an element of the double coset space $M$, where $M=T\\backslash SU(3)/T$, and $T=U(1)\\times U(1)$. The space $M$ is given a Riemannian metric, and has both point singularities, which it is shown correspond to the known renormalization group fixed points, and line singularities connecting the fixed points. A key discrete object inducing many of these properties is the Weyl group, $W$, of $SU(3)$, $W$ being the symmetric group $S_3$, which appears in the guise of the vertices of a hexagon in $V$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18884",
  "author_total": 2,
  "authors": [
    {
      "name": "Brian P. Dolan"
    },
    {
      "name": "Charles Nash"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cqf3p3khdnwb1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18884",
  "fulltext_url": null,
  "id": "cqf3p3khdnwb1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18884",
  "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|Particle physics theoretical and experimental studies"
    ]
  ],
  "openalex": "W7213501433",
  "pdf_url": "https://arxiv.org/pdf/2609.18884",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cqf3p3khdnwb1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.18884",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18884"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "The Geometry of the CKM matrix, the Standard Model and RG fixed points",
  "title_text": "The Geometry of the CKM matrix, the Standard Model and RG fixed points",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:19Z",
  "url": "https://research.draconitic.com/paper/cqf3p3khdnwb1",
  "venue": "arXiv",
  "versions": []
}