{
  "abstract": "We present a systematic study of finite, non-split 2-group symmetries with a non-trivial Postnikov class, focusing on the simplest example with a $\\mathbb{Z}_2$ 0-form symmetry and a $\\mathbb{Z}_2$ 1-form symmetry, intertwined together by the non-trivial Postnikov class in $H^3(B\\mathbb{Z}_2;\\mathbb{Z}_2)\\cong\\mathbb{Z}_2$, denoted by $\\mathcal{G}$. We classify the anomalies of this 2-group symmetry for physical theories in $d$-dimensional spacetime, by computing the oriented bordism groups $Ω_{d+1}^{\\rm SO}(B\\mathcal{G})$ and the spin bordism groups $Ω_{d+1}^{\\rm Spin}(B\\mathcal{G})$ for $d\\leq 5$. For the case of $d=3$, we investigate the Symmetry TFT/TO of the 2-group symmetry $\\mathcal{G}$ using the language of fusion 2-categories, as well as (3+1)D TQFT actions, for the cases without or with the 2-group anomaly classified by $\\operatorname{Hom}\\left(\\widetildeΩ_4^{\\rm SO}(B\\mathcal{G}),U(1)\\right) \\cong H^4(B\\mathcal{G};U(1))\\cong\\mathbb{Z}_2$. We classify the minimal topological and physical boundary conditions of the Symmetry TFTs, and carry out the categorical Landau paradigm for such a non-split finite 2-group.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.08766",
  "author_total": 4,
  "authors": [
    {
      "name": "Zhenbang Gu"
    },
    {
      "name": "Ran Luo"
    },
    {
      "name": "Yi-Nan Wang"
    },
    {
      "name": "Yi Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dgqk69aanwnq4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.08766",
  "fulltext_url": null,
  "id": "dgqk69aanwnq4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.08766",
  "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.AT"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7202188807",
  "pdf_url": "https://arxiv.org/pdf/2608.08766",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dgqk69aanwnq4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2608.08766",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.08766"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    },
    {
      "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": "Understanding Non-Split 2-Group Symmetry: (3+1)D SymTFT, Anomaly and Bordism",
  "title_text": "Understanding Non-Split 2-Group Symmetry: (3+1)D SymTFT, Anomaly and Bordism",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/dgqk69aanwnq4",
  "venue": "arXiv",
  "versions": []
}