{
  "abstract": "We compute the finite-$N$ Witten index of BMN matrix quantum mechanics after summing over all partition-labeled supersymmetric vacuum sectors. Starting from the unitary-matrix integral for each sector, we adapt two complementary evaluation methods to the BMN index: a symmetric-group character expansion, which reduces each fixed fugacity order to a finite combinatorial sum, and a residue expansion in which the contributing poles are organized by rooted trees, with a colored-tree generalization for multi-partition sectors. Where practical, direct integration and extraction of the constant term in the expanded integrand give independent coefficient-by-coefficient checks. We evaluate every vacuum sector for $N\\leq 9$. In the equal-fugacity expansion, the coefficients near charges $j\\sim N^2$ exhibit substantial cancellations between vacuum sectors, which tend to reduce the effective $N^2$ coefficient of the total index entropy. The finite-$N$ data also reveal a nontrivial sectoral organization: near $j=N^2$, the sector giving the largest contribution changes with $N$, from single-partition sectors at small rank to double-partition sectors starting at $N=6$. We call this phenomenon dominance switching. These results provide quantitative finite-$N$ input for using the BMN index as a diagnostic of protected plane-wave black-hole sectors and suggest in the controlled type-IIA regime a possible D2 dressed black-hole interpretation in which D0 black-hole sectors are accompanied by macroscopic spherical D2-brane degrees of freedom, analogous to dual dressed black holes in $AdS_5\\times S^5$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.25560",
  "author_total": 3,
  "authors": [
    {
      "name": "Chi-Ming Chang"
    },
    {
      "name": "Sarthak Duary"
    },
    {
      "name": "Kangning Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5qbrm7nkqqw5n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.25560",
  "fulltext_url": null,
  "id": "5qbrm7nkqqw5n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.25560",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7162456713",
  "pdf_url": "https://arxiv.org/pdf/2605.25560",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5qbrm7nkqqw5n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2605.25560",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.25560"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Finite-$N$ BMN index across all vacuum sectors",
  "title_text": "Finite-N BMN index across all vacuum sectors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:41Z",
  "url": "https://research.draconitic.com/paper/5qbrm7nkqqw5n",
  "venue": "arXiv",
  "versions": []
}