{
  "abstract": "The topologically twisted index of 3d ADHM theory can be written as a sum over solutions to the Bethe Ansatz Equations (BAEs) of the XXZ-type model constructed from quantum toroidal $\\mathfrak{g}\\mathfrak{l}_1$. Via a novel numerical algorithm, we solve for all $p(N)$ physical solutions at $N\\leq 21$, where $p(N)$ denotes the number of integer partitions of $N$. Surveying these solutions, we find that in addition to the known \"1-cut\" solution dual to dyonic black holes, where the gauge holonomies are distributed along a single curve in the complex plane, there are \"dressed\" 1-cut solutions dual to combined configurations of the black hole and M2-branes, $m$-cut solutions dual to $\\mathbb{Z}_m$ orbifolds of the black hole, a discrete family of solutions interpolating between the 1-cut and 3-cut solutions, together with other exotic solutions, at each value of $N$. The free energy of the interpolating solutions cannot be matched with the on-shell action of any known bulk solution. The $1,2,3$-cut solutions and interpolating solutions all have a well-defined large $N$ limit, and their leading order distribution of gauge holonomies can be computed analytically. Whenever possible, we fit the contributions of the solutions to the index to all orders in the $1/N$ expansion with high-precision numerics, and extract the leading non-perturbative correction. With exceptions, these are matched with the results of equivariant localization in the bulk, and the action of wrapped M2-branes respectively.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27097",
  "author_total": 3,
  "authors": [
    {
      "name": "Cheng Peng"
    },
    {
      "name": "Xuao Zhang"
    },
    {
      "name": "Ziruo Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9a5vr03drz1qp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27097",
  "fulltext_url": null,
  "id": "9a5vr03drz1qp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27097",
  "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"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7223120403",
  "pdf_url": "https://arxiv.org/pdf/2610.27097",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9a5vr03drz1qp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.27097",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27097"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Mapping AdS$_4$ quantum gravity via the Bethe Ansatz formula",
  "title_text": "Mapping AdS_4 quantum gravity via the Bethe Ansatz formula",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/9a5vr03drz1qp",
  "venue": "arXiv",
  "versions": []
}