{
  "abstract": "We study the perturbative S S -matrix of the c=1 c = 1 string and show that it admits a description in terms of a double-scaled (0+0)-dimensional matrix integral based on the spectral curve \\mathsf{x}(z) = 2\\sqrt{2}\\cos(z) 𝗑 ( z ) = 2 2 cos ⁡ ( z ) , \\mathsf{y}(z)=\\sin(z) 𝗒 ( z ) = sin ⁡ ( z ) . Combined with the famous duality to matrix quantum mechanics, this establishes a triality between three formulations of the theory: the worldsheet description, matrix quantum mechanics, and a matrix integral. Starting from the intersection number expressions for the complex Liouville string, we derive closed-form Feynman rule expressions for the c=1 c = 1 amplitudes as intersection numbers on the moduli space of Riemann surfaces. The intersection theory naturally computes amplitudes corresponding to a discretized target space where momentum is conserved only modulo an integer. The physical S S -matrix elements are recovered by restriction to the first `Brillouin zone’ and analytic continuation to Lorentzian kinematics. We prove that these amplitudes satisfy perturbative spacetime unitarity directly from the intersection theory expressions, and show that they satisfy a Mirzakhani-type recursion relation. We show detailed agreement with the known matrix quantum mechanics results, providing strong evidence for the triality.",
  "abstract_shown": true,
  "affiliations": [
    "Syracuse University",
    "Institute for Theoretical Physics Amsterdam",
    "University of California, Santa Barbara"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Scott Collier",
      "orcid": "0000-0002-8647-6653"
    },
    {
      "affs": [
        1
      ],
      "name": "Lorenz Eberhardt",
      "orcid": "0000-0003-1912-2211"
    },
    {
      "affs": [
        2
      ],
      "name": "Victor A. Rodriguez",
      "orcid": "0000-0002-2980-0621"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1tp1s9g12xgdp.bib",
  "cited_by": 1,
  "doi": "10.21468/scipostphys.21.4.085",
  "fulltext_url": null,
  "id": "1tp1s9g12xgdp",
  "issns": [
    "2542-4653"
  ],
  "landing_url": "https://scipost.org/10.21468/SciPostPhys.21.4.085",
  "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": "W7152503335",
  "pdf_url": "https://scipost.org/10.21468/SciPostPhys.21.4.085/pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": "Stichting SciPost",
  "ris": "https://research.draconitic.com/paper/1tp1s9g12xgdp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:57Z",
      "native_id": "10.21468/scipostphys.21.4.085",
      "source": "crossref",
      "url": "https://scipost.org/10.21468/SciPostPhys.21.4.085"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3106|Black Holes and Theoretical Physics",
      "subfield": "high-energy"
    }
  ],
  "title": "$c=1$ strings as a matrix integral",
  "title_text": "c=1 strings as a matrix integral",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:57Z",
  "url": "https://research.draconitic.com/paper/1tp1s9g12xgdp",
  "venue": "SciPost Physics",
  "versions": []
}