{
  "abstract": "Five-dimensional $\\mathcal{N}=1$ superconformal field theories admit a rich variety of generalised global symmetries, including higher-form and 2-group symmetries and their 't$~$Hooft anomalies. We show that this data can be extracted directly from the blow-up equations governing the instanton partition functions of such theories on the $Ω$-background. The central object is the classical prefactor $\\exp(-V_n)$ weighting each magnetic flux on the blown-up geometry: evaluated on a background for the electric 1-form symmetry, the fractional parts of its exponents encode the cubic self-anomaly of the 1-form symmetry and its mixed anomalies with the instanton, flavour, gravitational, and $\\mathrm{SU}(2)_R$ symmetries. Combined with the faithful continuous global symmetry of the ultraviolet fixed point, determined from the superconformal index, the same data decides whether the theory possesses a 2-group symmetry or a mixed 't$~$Hooft anomaly. We illustrate the method in gauge theories, including $\\mathrm{SU}(4)$ and $\\mathrm{USp}(4)$ with antisymmetric hypermultiplets and $\\mathrm{Spin}(7)$ and $\\mathrm{Spin}(8)$ with vector hypermultiplets, as well as in several families of non-Lagrangian theories. New results include the effective prepotentials of the $B_N$ and $B_N^{(1,2,3)}$ families, the cubic 1-form anomalies of the rank-two theories $\\mathbb{P}^2\\cup\\mathbb{F}_3$ and $\\mathbb{P}^2\\cup\\mathbb{F}_6$, and several mixed 1-form--flavour and 1-form--$\\mathrm{SU}(2)_R$ anomalies.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: JHEP09(2026)248",
  "arxiv": "2607.06663",
  "author_total": 2,
  "authors": [
    {
      "name": "William Harding"
    },
    {
      "name": "Noppadol Mekareeya"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3x98t3hd3x760.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.06663",
  "fulltext_url": null,
  "id": "3x98t3hd3x760",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.06663",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2607.06663",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3x98t3hd3x760.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2607.06663",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.06663"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Generalised global symmetries in 5d $\\mathcal{N}=1$ theories from the blow-up equations",
  "title_text": "Generalised global symmetries in 5d 𝒩=1 theories from the blow-up equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:11Z",
  "url": "https://research.draconitic.com/paper/3x98t3hd3x760",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1007/jhep09(2026)248",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}