{
  "abstract": "We construct a solution of seven-dimensional maximal gauged supergravity of the form AdS$_2\\times M_5$, where $M_5$ is the five-dimensional Wu manifold $SU(3)/SO(3)$. The solution is supersymmetric, despite the fact that the Wu manifold admits neither a spin structure nor a spin$^c$ structure. Rather, it admits a spin$^h$ structure, wherein the ill-definedness of ordinary spinors due to a minus sign in their holonomy is compensated by a further minus sign arising through the spinors carrying $SO(3)$ Yang-Mills charge, in a half-integer isospin representation of the $SU(2)$ double cover of the $SO(3)$. We show how the configuration can be lifted to a solution of $D=11$ supergravity of the form AdS$_2\\times M_9$, where $M_9$ is the unit tangent bundle of the Wu manifold. We discuss the geometry and topology of $M_9$, and study the supersymmetry from the eleven-dimensional standpoint. We extend the seven-dimensional solution to a black hole, and discuss some aspects of its holographic interpretation and the UV to IR flow. We revisit a previously-known AdS$_2\\times H^3\\times H^2$ solution, and its UV to IR flow, showing that the flow equations in fact admit of an exact solution. Additionally, we give a detailed discussion of the lift of the AdS$_2\\times S^5$ solution to $D=11$, exhibiting similarities and differences between the properties of its internal space $M_9$ (the unit tangent bundle of $S^5$) and the Wu manifold example of our main discussion. We also construct the non-compact dual of the Wu manifold solution, where $M_5$ is taken to be $SL(3,\\mathbb R)/SO(3)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24084",
  "author_total": 3,
  "authors": [
    {
      "name": "Cameron Gibson"
    },
    {
      "name": "Okan Günel"
    },
    {
      "name": "C. N. Pope"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4a1fge7v2hpre.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24084",
  "fulltext_url": null,
  "id": "4a1fge7v2hpre",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24084",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7223013254",
  "pdf_url": "https://arxiv.org/pdf/2610.24084",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4a1fge7v2hpre.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.24084",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24084"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Wrapping M5-branes on a non-spin manifold: Spin$^h$ structures and AdS$_7$ black holes",
  "title_text": "Wrapping M5-branes on a non-spin manifold: Spin^h structures and AdS_7 black holes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:04Z",
  "url": "https://research.draconitic.com/paper/4a1fge7v2hpre",
  "venue": "arXiv",
  "versions": []
}