{
  "abstract": "We investigate non-invertible selection rules originating from the discrete $H$-gauging of theories with an underlying discrete global symmetry group $G$. To systematically describe these theories, we formulate a general framework for $H$-gauged models that incorporates generalized field transformations. Our approach naturally accommodates non-Abelian groups, for which multidimensional irreducible representations play an essential role. In such models with non-Abelian groups, the transformations induced by $H$ non-trivially mix the internal components of $G$-multiplets, potentially projecting out specific degrees of freedom. Consequently, conventional selection rules based on standard tensor product decompositions or conjugacy classes become insufficient. By analyzing the full semidirect product $G \\rtimes H$, we introduce projected characters to derive necessary and sufficient conditions for non-vanishing $n$-point bare couplings. Furthermore, we demonstrate that the remaining field components obey an associative fusion-like algebra governed by their Clebsch-Gordan coefficients. Phenomenologically, these selection rules restrict allowed interactions and impose specific relations among coupling constants. We illustrate our results through concrete examples, including $Δ(54) \\cong Δ(27)\\rtimes \\mathbb{Z}_2$ and $S_4 \\cong A_4 \\rtimes \\mathbb{Z}_2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11895",
  "author_total": 2,
  "authors": [
    {
      "name": "Hiroshi Ohki"
    },
    {
      "name": "Shohei Uemura"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3c2z60ckfv9qz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11895",
  "fulltext_url": null,
  "id": "3c2z60ckfv9qz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11895",
  "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-ph"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Particle physics theoretical and experimental studies"
    ]
  ],
  "openalex": "W7212283849",
  "pdf_url": "https://arxiv.org/pdf/2609.11895",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3c2z60ckfv9qz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:52Z",
      "native_id": "2609.11895",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11895"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "Non-invertible Selection Rules from Generalized Discrete Gauging of Finite Non-Abelian Symmetries",
  "title_text": "Non-invertible Selection Rules from Generalized Discrete Gauging of Finite Non-Abelian Symmetries",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:52Z",
  "url": "https://research.draconitic.com/paper/3c2z60ckfv9qz",
  "venue": "arXiv",
  "versions": []
}