{
  "abstract": "We study three-dimensional $BF$ theory as the large-level limit of the doubled Chern--Simons theory $G_k\\times G_{-k}$ for simply connected, compact, simple $G$, a limit that connects the symmetry topological field theories of finite and continuous symmetries. Lines whose two highest weights grow linearly with $k$ at fixed difference become $BF$ lines, with magnetic flux set by their average and electric charge equal to their difference. Representing level-$k$ torus states as normalized flux--charge wave packets, we prove that every fixed modular transformation of any fixed normalizable state with regular flux converges in the strong-$*$ topology to its $BF$ counterpart. The Dehn twist gives each line exactly its Aharonov--Bohm phase at every level, while $S$ converges to a Fourier transform exchanging flux and charge, without escaping to singular holonomies or large charges. States that approach singular fluxes at large $k$ are not covered. The natural boundary 2d theory is speculated to be a decompactified boson in the abelian case $G=U(1)$, and $\\dim G$ non-compact free scalars for general $G$. For $SU(2)$, we discuss the gapped interfaces between adjacent levels, which must shift some flux or charge by a finite amount. In the $k\\rightarrow\\infty$ limit the interface is conjectured to be the $c=1$ Runkel--Watts theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26735",
  "author_total": 4,
  "authors": [
    {
      "name": "Shengyi Guan"
    },
    {
      "name": "Qiang Jia"
    },
    {
      "name": "Jiahua Tian"
    },
    {
      "name": "Yi-Nan Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/06s0nqxv8cyd7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26735",
  "fulltext_url": null,
  "id": "06s0nqxv8cyd7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26735",
  "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"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7223069865",
  "pdf_url": "https://arxiv.org/pdf/2610.26735",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/06s0nqxv8cyd7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2610.26735",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26735"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Large-Level Limit of Doubled Chern-Simons Theory Part I: Regular Sector, Boundaries and Interfaces",
  "title_text": "Large-Level Limit of Doubled Chern-Simons Theory Part I: Regular Sector, Boundaries and Interfaces",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/06s0nqxv8cyd7",
  "venue": "arXiv",
  "versions": []
}