{
  "abstract": "Matrix models appear as fundamental descriptions of M-theory and D-brane dynamics, and via the gauge/gravity duality their gauge-invariant, or singlet, sector describes the purely gravitational degrees of freedom in the holographic dual. We present a new exact algorithm for computing observables of bosonic U(N) matrix models in the gauge-invariant singlet sector. This sector is spanned by an orthogonal basis of Schur polynomials (for a single matrix) and restricted Schur polynomials (for multiple matrices), which diagonalizes the free Hamiltonian and provides a natural truncation of the Hilbert space by excitation number. Matrix elements of the interaction Hamiltonian, or any gauge-invariant observable, are evaluated through a group-theoretic reduction to cosets and double cosets of suitable subgroups of the symmetric group, together with character sums on the symmetric group. The resulting entries are closed-form polynomials in the gauge-group rank N, assembled from group-theoretic data that are precomputed once and can be reused for any N and any coupling constants. We validate the one-matrix implementation against the exact mapping to N non-interacting fermions, demonstrating rapid convergence of the low-lying spectrum with the cutoff. The multi-matrix extension is outlined; its main bottleneck is the computation of restricted characters of the symmetric group, for which no algorithm comparable to the Murnaghan--Nakayama rule is currently known. The framework gives direct access to finite-N, finite-coupling dynamics of gauge-invariant states and opens a new computational window on the non-planar regime of holographic matrix models.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: JHEP 10 (2026) 048",
  "arxiv": "2607.13725",
  "author_total": 2,
  "authors": [
    {
      "name": "Enrico M. Brehm"
    },
    {
      "name": "Jean Cazalis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/asdrbs4wg5nnt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.13725",
  "fulltext_url": null,
  "id": "asdrbs4wg5nnt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.13725",
  "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"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2607.13725",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/asdrbs4wg5nnt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:37Z",
      "native_id": "2607.13725",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.13725"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "An exact algorithm for U(N) matrix models in the gauge-invariant singlet sector",
  "title_text": "An exact algorithm for U(N) matrix models in the gauge-invariant singlet sector",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/asdrbs4wg5nnt",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1007/jhep10(2026)048",
      "pid": "aepcr0v558tmn",
      "relation": "published-as",
      "title": "An exact algorithm for U(N) matrix models in the gauge-invariant singlet sector",
      "venue": "Journal of High Energy Physics"
    }
  ]
}