{
  "abstract": "We study finite-$N$ coherent-state overlap kernels in multi-matrix BPS sectors of $\\mathcal N=4$ super Yang--Mills theory. For commuting coherent-state parameters, the kernel is a Laplace transform of the Haar-pushforward measure on the unistochastic set. After quotienting row- and column-shift redundancies, the nontrivial source is an $(N-1)\\times(N-1)$ matrix $D$. On the physical $m$-matrix locus, $D$ is a Gram matrix with $\\operatorname{rank}D\\leq m$, and the ordinary HCIZ sector is precisely the rank-at-most-one stratum. For $N=3$ we obtain an exact Bessel-integral representation of the first genuinely rank-two kernel. Along the rank-one ray $D=rE_{11}$, $F_N={}_1F_1(1;N;r)$ for arbitrary finite $N$. Using $K_N=\\log F_N$ as the reduced Kähler potential, we study a controlled two-matrix embedding of the HCIZ sector and determine its transverse metric, second fundamental form, and Gauss--Codazzi geometry. The embedding is non-totally-geodesic at finite $N$. In the scaling $r=Nρ$, we find \\begin{equation} Nh_N\\to\\min(ρ,1), \\qquad \\|B\\|^2\\to2(1-ρ)_+. \\end{equation}",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24483",
  "author_total": 1,
  "authors": [
    {
      "name": "Shannon Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ccavd203bjzn7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24483",
  "fulltext_url": null,
  "id": "ccavd203bjzn7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24483",
  "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",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7214047188",
  "pdf_url": "https://arxiv.org/pdf/2609.24483",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ccavd203bjzn7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2609.24483",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24483"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Unistochastic reduction of multi-matrix coherent-state kernels",
  "title_text": "Unistochastic reduction of multi-matrix coherent-state kernels",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:03Z",
  "url": "https://research.draconitic.com/paper/ccavd203bjzn7",
  "venue": "arXiv",
  "versions": []
}