{
  "abstract": "A bstract We define the symmetry category in 1+1d for continuous 0-form G -symmetry to be Sky τ ( G ), the category of skyscraper sheaves of finite dimensional vector spaces with finite support on the group manifold of G , where τ ∈ H 4 ( BG, ℤ) is the anomaly. We propose that the corresponding 2+1d SymTFT is described by the Drinfeld center of Sky τ ( G ). We show explicitly the way that τ twists the convolution tensor product of the objects of Sky τ ( G ). As a concrete example, we present the S and T -matrices for the simple anyons of the resulting Z ( Sky τ ( G )) category for G = U (1), both for the cases without or with anomaly, and discuss the topological boundary conditions as Lagrangian algebra of Z ( Sky τ ( U (1))). We also present the definition of Sky τ ( G ) and Z ( Sky τ ( G )) for the non-abelian case of G = SU (2), as well as the speculated modular data. We point out that in order to have a physically relevant center and Lagrangian algebras, it is necessary to generalize Sky τ ( G ) to a larger category, which we argue to be closely related to the category of quasi-coherent sheaves on G ℂ with convolution tensor product twisted by τ .",
  "abstract_shown": true,
  "affiliations": [
    "Korea Advanced Institute of Science Technology",
    "Peking University",
    "Perimeter Institute for Theoretical Physics",
    "East China Normal University",
    "The University of Tokyo"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 5,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Qiang Jia",
      "orcid": "0009-0002-1890-8431"
    },
    {
      "affs": [
        1,
        2
      ],
      "name": "Ran Luo",
      "orcid": "0009-0004-5747-8969"
    },
    {
      "affs": [
        3
      ],
      "name": "Jiahua Tian",
      "orcid": "0000-0001-7407-7535"
    },
    {
      "affs": [
        1
      ],
      "name": "Yi-Nan Wang",
      "orcid": "0000-0001-7418-1519"
    },
    {
      "affs": [
        4
      ],
      "name": "Yi Zhang A",
      "orcid": "0000-0002-0125-0998"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/frvjvmdbjdm13.bib",
  "cited_by": 12,
  "doi": "10.1007/jhep06(2026)031",
  "fulltext_url": null,
  "id": "frvjvmdbjdm13",
  "issns": [
    "1029-8479",
    "1126-6708",
    "1127-2236"
  ],
  "landing_url": "https://doi.org/10.1007/jhep06(2026)031",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W4415317643",
  "pdf_url": "https://link.springer.com/content/pdf/10.1007/JHEP06(2026)031.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-03",
  "publisher": "Springer Nature",
  "ris": "https://research.draconitic.com/paper/frvjvmdbjdm13.ris",
  "sources": [
    {
      "first_seen": "2026-11-07T13:20:42Z",
      "native_id": "W4415317643",
      "source": "openalex",
      "url": "https://doi.org/10.1007/jhep06(2026)031"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Algebraic structures and combinatorial models",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Categorical continuous symmetry",
  "title_text": "Categorical continuous symmetry",
  "type": "peer-reviewed",
  "updated_at": "2026-11-08T13:20:36Z",
  "url": "https://research.draconitic.com/paper/frvjvmdbjdm13",
  "venue": "Journal of High Energy Physics",
  "versions": []
}