{
  "abstract": "In this article, we give a global construction of the Virasoro conformal blocks on Teichmüller space of Riemann surfaces of genus $g$ with $m$ marked points, when the central charge is $c>25$. We prove that they are global holomorphic sections of a holomorphic line bundle and they satisfy the Ward identity, which encodes their conformal invariance. For the sphere with $3$ points, the space of conformal blocks is one-dimensional. For a given marked Riemann surface and a marked pair of pants decomposition, it is in general an infinite dimensional Hilbert space, isomorphic to $L^2(\\R_+^{3g-3+m})$ with respect to some measure involving the DOZZ structure constants. We show that it carries a projective unitary representation of the mapping class group. More generally, there are unitary isomorphisms for each Moore-Seiberg move, changing a marked pair of pants decomposition into another one.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03540",
  "author_total": 5,
  "authors": [
    {
      "name": "Guillaume Baverez"
    },
    {
      "name": "Colin Guillarmou"
    },
    {
      "name": "Antti Kupiainen"
    },
    {
      "name": "Rémi Rhodes"
    },
    {
      "name": "Yuxiao Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ccvra4qjkyp5f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03540",
  "fulltext_url": null,
  "id": "ccvra4qjkyp5f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03540",
  "language": "en",
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
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      "arxiv",
      "math.SP"
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    [
      "hal",
      "0.math"
    ],
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      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7220473435",
  "pdf_url": "https://arxiv.org/pdf/2610.03540",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ccvra4qjkyp5f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.03540",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03540"
    },
    {
      "first_seen": "2026-11-02T12:20:44Z",
      "native_id": "hal-05847177",
      "source": "hal",
      "url": "https://hal.science/hal-05847177v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Virasoro Conformal Blocks and modular functor from Liouville CFT",
  "title_text": "Virasoro Conformal Blocks and modular functor from Liouville CFT",
  "type": "preprint",
  "updated_at": "2026-11-03T12:20:17Z",
  "url": "https://research.draconitic.com/paper/ccvra4qjkyp5f",
  "venue": "arXiv",
  "versions": []
}