{
  "abstract": "We study flat gauging of continuous symmetries by summing over flat gauge-field configurations. We focus on the two-dimensional compact boson and construct the torus partition function with general flat $U(1)_M\\times U(1)_W$ backgrounds. We show that flat gauging either $U(1)_M$ or $U(1)_W$ decompactifies the theory to the non-compact free boson, and that the dual $\\mathbb{Z}$ background combines with the remaining $U(1)$ background into a non-compact $\\mathbb{R}$ symmetry background due to the mixed anomaly. We also revisit the self-dual radius, where flat gauging the diagonal $SO(3)\\subset (SU(2)_L\\times SU(2)_R)/\\mathbb{Z}_2$, first pointed out by Gaberdiel and Suchanek, gives the continuous orbifold which lies outside the usual $c=1$ moduli space. On the orbifold branch, we study finite and continuous non-invertible flat gaugings and explain why the continuous case requires a prescription for zero-measure fixed loci on the moduli space. Finally, we formulate the SymTFT of torus sigma models as a non-compact BF theory, whose topological boundary states encode the Narain moduli space and the $O(D,D;\\mathbb{Z})$ T-duality action.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.15732",
  "author_total": 2,
  "authors": [
    {
      "name": "Qiang Jia"
    },
    {
      "name": "Yi Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/34b6qedtb8kjx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.15732",
  "fulltext_url": null,
  "id": "34b6qedtb8kjx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.15732",
  "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|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7164892955",
  "pdf_url": "https://arxiv.org/pdf/2606.15732",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/34b6qedtb8kjx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2606.15732",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.15732"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Flat Gauging of Continuous (Non-invertible) Symmetries and Non-compact BF SymTFT for Compact Boson",
  "title_text": "Flat Gauging of Continuous (Non-invertible) Symmetries and Non-compact BF SymTFT for Compact Boson",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/34b6qedtb8kjx",
  "venue": "arXiv",
  "versions": []
}