{
  "abstract": "Exploiting newly available data on Gopakumar-Vafa invariants at high genus for one-parameter hypergeometric Calabi-Yau threefolds, we study numerically the growth of the 5D indices, stable pair (PT) invariants and rank one Donaldson-Thomas (DT) invariants at large charges. For the 5D index $Ω_{5D}(d,m)$, below a critical value of the angular momentum $m$, we find perfect agreement with the Bekenstein-Hawking-Wald entropy of rotating 5D BMPV black holes, including the subleading correction from four-derivative interactions. When $m$ exceeds the critical value, the 5D index is instead dominated by black rings with the smallest possible dipole charge. The stable pair invariant $PT(d,m)$, which is determined by 5D indices, has a similar black ring/hole transition at negative $m$ (now interpreted as the D0-brane charge) but surprisingly exhibits two other phase transitions at positive $m$: first, to a plateau and then to a polynomial growth $\\sim m^{2d-1}$. In each phase, we derive an approximate expression for the invariant. Finally, the rank one DT invariant $DT(d,m)$ is similar to $PT(d,m)$ at negative $m$, and then transitions to a phase dominated by D0-branes, with entropy of order $m^{2/3}$. Along the way, we determine the fixed genus, large degree behavior of GV invariants (including the overall $g$-dependent constant), extend it to an approximate formula valid also for large $g$, point out the unreasonable effectiveness of a simple PT/MSW relation, and study the growth of topological free energies at fixed degree, confirming a conjecture of Mariño.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.19552",
  "author_total": 3,
  "authors": [
    {
      "name": "Sergei Alexandrov"
    },
    {
      "name": "Albrecht Klemm"
    },
    {
      "name": "Boris Pioline"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c0ys6e66qp1qn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.19552",
  "fulltext_url": null,
  "id": "c0ys6e66qp1qn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.19552",
  "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"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7161760949",
  "pdf_url": "https://arxiv.org/pdf/2605.19552",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c0ys6e66qp1qn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2605.19552",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.19552"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Large Order Enumerative Geometry, Black Holes and Black Rings",
  "title_text": "Large Order Enumerative Geometry, Black Holes and Black Rings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/c0ys6e66qp1qn",
  "venue": "arXiv",
  "versions": []
}