{
  "abstract": "A bstract : 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": [
    "Deutsches Elektronen-Synchrotron DESY"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Enrico Brehm",
      "orcid": "0000-0001-7523-7027"
    },
    {
      "affs": [
        0
      ],
      "name": "Jean Cazalis",
      "orcid": "0009-0000-1489-7566"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aepcr0v558tmn.bib",
  "cited_by": 0,
  "doi": "10.1007/jhep10(2026)048",
  "fulltext_url": null,
  "id": "aepcr0v558tmn",
  "issns": [
    "1029-8479"
  ],
  "landing_url": "https://link.springer.com/10.1007/JHEP10(2026)048",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7168599197",
  "pdf_url": "https://link.springer.com/content/pdf/10.1007/JHEP10(2026)048.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": "Springer Science and Business Media LLC",
  "ris": "https://research.draconitic.com/paper/aepcr0v558tmn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:01Z",
      "native_id": "10.1007/jhep10(2026)048",
      "source": "crossref",
      "url": "https://link.springer.com/10.1007/JHEP10(2026)048"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3106|Black Holes and Theoretical Physics",
      "subfield": "high-energy"
    }
  ],
  "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": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:01Z",
  "url": "https://research.draconitic.com/paper/aepcr0v558tmn",
  "venue": "Journal of High Energy Physics",
  "versions": [
    {
      "doi": "10.48550/arxiv.2607.13725",
      "pid": "asdrbs4wg5nnt",
      "relation": "preprint",
      "title": "An exact algorithm for U(N) matrix models in the gauge-invariant singlet sector",
      "venue": "arXiv"
    }
  ]
}