{
  "abstract": "We study the rank-two logarithmic sector of critical Topologically Massive Gravity through the Virasoro zero-mode action \\[ U(s,\\bar s)=e^{-sL_0-\\bar s\\bar L_0}. \\] Writing $L_0=h\\mathbf 1+\\frac{1}{2}N$ and $\\bar L_0=\\bar h\\mathbf 1+\\frac{1}{2}N$, with $N^2=0$, separates the semisimple conformal grading from the nilpotent mixing of the logarithmic pair. We apply the Virasoro zero-mode action to logarithmic two-point functions and to the conformal grading of the logarithmic contribution to the one-loop partition function. For the correlators, the semisimple part generates the ordinary conformal power law, while the nilpotent mixing governed by the combination $s+\\bar s$ produces the characteristic logarithmic dependence. For the critical-TMG weights $(h,\\bar h)=(2,0)$, this gives a holomorphic power law together with logarithmic dependence on the full Euclidean separation. For the partition function, the relations $q=e^{-s}$ and $\\bar q=e^{-\\bar s}$ express its conventional multiplicative grading in terms of the additive parameters of the same Virasoro zero-mode action, providing an exact reparameterization of the established one-loop result. The two applications capture complementary information: logarithmic correlators resolve the off-diagonal Jordan mixing, whereas the ordinary graded trace organizes conformal weights, multiplicities, and descendant content without separately resolving the nilpotent matrix element. The Virasoro zero-mode action therefore provides a unified representation-theoretic description of these boundary structures in critical TMG.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.03649",
  "author_total": 1,
  "authors": [
    {
      "name": "Yannick Mvondo-She"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6b3a8j9t1bmx1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.03649",
  "fulltext_url": null,
  "id": "6b3a8j9t1bmx1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.03649",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7160391479",
  "pdf_url": "https://arxiv.org/pdf/2605.03649",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6b3a8j9t1bmx1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:26Z",
      "native_id": "2605.03649",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.03649"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Virasoro Zero-Mode Flow in Critical Topologically Massive Gravity: Logarithmic Correlators and Partition Function Grading",
  "title_text": "Virasoro Zero-Mode Flow in Critical Topologically Massive Gravity: Logarithmic Correlators and Partition Function Grading",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:26Z",
  "url": "https://research.draconitic.com/paper/6b3a8j9t1bmx1",
  "venue": "arXiv",
  "versions": []
}