{
  "abstract": "We establish a refined Ryu--Takayanagi (RT) relation in AdS$_3$/CFT$_2$ using \\emph{relative entropy} as the central object, in place of the ultraviolet-divergent von Neumann entanglement entropy. Adapting Hollands' exact result for the chiral relative entropy to a diamond region, we express the boundary relative entropy between the vacuum and a coherent state as a Schwarzian functional, which the Fefferman--Graham dictionary identifies with the asymptotic data of a Bañados geometry; the rigidity of three-dimensional gravity promotes this boundary identification to the bulk. To linear order in the metric perturbation, the relative entropy then equals the variation of the RT geodesic length divided by $4G_N$. The construction rests only on the Bisognano--Wichmann/Borchers theorem and the holographic dictionary, giving a UV-finite, operator-algebraic counterpart to the RT relation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.27915",
  "author_total": 4,
  "authors": [
    {
      "name": "Philipp Dorau"
    },
    {
      "name": "Albert Much"
    },
    {
      "name": "Leonardo Sangaletti"
    },
    {
      "name": "Rainer Verch"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/74avvqn4hqj9j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.27915",
  "fulltext_url": null,
  "id": "74avvqn4hqj9j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.27915",
  "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",
      "gr-qc"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7166548866",
  "pdf_url": "https://arxiv.org/pdf/2606.27915",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/74avvqn4hqj9j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:32Z",
      "native_id": "2606.27915",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.27915"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "A UV-Finite Refinement of the Ryu-Takayanagi Relation in AdS$_3$/CFT$_2$",
  "title_text": "A UV-Finite Refinement of the Ryu-Takayanagi Relation in AdS_3/CFT_2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/74avvqn4hqj9j",
  "venue": "arXiv",
  "versions": []
}