{
  "abstract": "The sewing operation is the fundamental algebraic structure of the (infinite-dimensional) Segal moduli spaces as the conformal cobordism category. We prove a universal property of local $\\mathbb{R}_+$-extensions of the sewing operation, characterizing them by one real parameter: their central charge. Our result is an analogue of ``Mumford's theorem,'' that appeared in Segal's monograph [Seg88, Seg04], classifying complex extensions, also known as one-dimensional modular functors. Algebraically, the real extensions are characterized by real-valued cocycles on pairs of surfaces under sewing. We identify the disk-disk cocycle as the universal Liouville action, also known as loop Loewner energy. The real determinant line bundle encodes the trace anomaly of euclidean two-dimensional conformal field theories (CFT) and the restriction function of Schramm-Loewner evolution (SLE) loop measures. It serves as the guiding example in our setup and proof strategy, providing the universal $\\mathbb{R}_+$-extension. Our results thus give a mathematical explanation for the appearance of the central charge in CFT and SLE, and prove the conjectured uniqueness of Brownian loop measures as the canonical restriction function for SLE.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.23201",
  "author_total": 2,
  "authors": [
    {
      "name": "Sid Maibach"
    },
    {
      "name": "Eveliina Peltola"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2pwb8esfdps6e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.23201",
  "fulltext_url": null,
  "id": "2pwb8esfdps6e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.23201",
  "language": null,
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7204201734",
  "pdf_url": "https://arxiv.org/pdf/2608.23201",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2pwb8esfdps6e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:31Z",
      "native_id": "2608.23201",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.23201"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Universality of the conformal anomaly",
  "title_text": "Universality of the conformal anomaly",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/2pwb8esfdps6e",
  "venue": "arXiv",
  "versions": []
}