{
  "abstract": "We study the dual quantum symmetry $\\mathrm{Rep}(G)$ in the two-dimensional theory $\\widetilde{\\mathfrak{T}}_{\\mathrm{Rep}(G)}$ obtained by gauging a non-abelian symmetry $G$ of $\\mathfrak{T}_G$, where for Lie groups $G$ the gauging is understood as flat gauging. We develop a general framework for computing partition functions of $\\widetilde{\\mathfrak{T}}_{\\mathrm{Rep}(G)}$ in arbitrary non-invertible symmetry backgrounds, represented by topological defect networks of $\\mathrm{Rep}(G)$, in terms of the partition functions of the original theory $\\mathfrak{T}_G$. We also derive the inverse transformation, expressing partition functions of $\\mathfrak{T}_G$ in $G$ backgrounds in terms of those of $\\widetilde{\\mathfrak{T}}_{\\mathrm{Rep}(G)}$. We test the framework in several examples, including finite groups with multiplicity-free and higher-multiplicity fusion rules, and discuss a formal extension to compact Lie groups, focusing on $\\mathrm{Rep}(SU(2))$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09550",
  "author_total": 2,
  "authors": [
    {
      "name": "Jin Chen"
    },
    {
      "name": "Qiang Jia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6jqgyy93ph5hz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09550",
  "fulltext_url": null,
  "id": "6jqgyy93ph5hz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09550",
  "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",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7212171879",
  "pdf_url": "https://arxiv.org/pdf/2609.09550",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6jqgyy93ph5hz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2609.09550",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09550"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "On general background of quantum non-invertible symmetry in 2D",
  "title_text": "On general background of quantum non-invertible symmetry in 2D",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:12Z",
  "url": "https://research.draconitic.com/paper/6jqgyy93ph5hz",
  "venue": "arXiv",
  "versions": []
}