{
  "abstract": "Recent work has constructed Abelian Chern-Simons theories as categorical TQFTs, allowing us to naturally incorporate categorical defects and construct defect extensions of Abelian Chern-Simons TQFTs. We first identify the Turaev-Viro realizations of Abelian Chern-Simons theory in the center and doubled pointed modular cases, clarifying the distinction between single bulk realizations and canonical doubled ones. Then we obtain Turaev-Viro partition functions in terms of Reidemeister-torsion densities. Alternatively, the Alterfold construction supplies the associated topological boundaries, domain walls, and condensation sectors, establishing an explicit Alterfold/Chern-Simons dictionary. We show that the finite quadratic module is the invariant controlling the bulk theory, its topological symmetries, orientation-reversal invariance, and defects. We further show that multicomponent Abelian BF theory arises as the extended TQFT of an off-diagonal Abelian Chern-Simons theory, placing it naturally within the same extended framework. Finally, we demonstrate that recently proposed Abelian Chern-Simons dualities do not define a genuine TQFT duality. These results provide a concrete model for defects in Abelian topological orders and suggest a route toward the non-Abelian case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21414",
  "author_total": 1,
  "authors": [
    {
      "name": "Daniel Galviz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1wntcrxze2kjd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21414",
  "fulltext_url": null,
  "id": "1wntcrxze2kjd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21414",
  "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",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7213949783",
  "pdf_url": "https://arxiv.org/pdf/2609.21414",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1wntcrxze2kjd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:50Z",
      "native_id": "2609.21414",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21414"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "A Functorial Theory of Defects in Abelian Chern-Simons Theory",
  "title_text": "A Functorial Theory of Defects in Abelian Chern-Simons Theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/1wntcrxze2kjd",
  "venue": "arXiv",
  "versions": []
}