{
  "abstract": "We derive a $2d$ effective action for semi-classical AdS$_3$ gravity with an EOW brane of arbitrary tension by solving the radial Hamiltonian flow in a derivative expansion. Interpreting the radial flow as an RG flow, the effective theory is identified with a $T\\bar T$-like deformed CFT. This leads us to propose that the holographic dual for semi-classical AdS$_3$ gravity with Neumann or conformal boundary conditions is obtained by setting the $T\\bar T$-like deformed CFT free. We verify our proposal explicitly for saddles corresponding to $(A)dS_2$ branes in empty AdS$_3$. We discuss three useful ways to decompose the effective brane theory into a matter sector ($T\\bar T$-deformed, $T\\bar T$-like deformed, and undeformed CFT, respectively) and a corresponding braneworld gravity sector. In particular, the split into $T\\bar T$-deformed CFT coupled to $T\\bar T$-like deformed Liouville gravity directly extends the Liouville description of the integrated Weyl anomaly into the bulk. The effective action is then used to perform an island-rule calculation for a non-asymptotic brane in an AdS/bCFT set-up, finding exact agreement with the Ryu-Takayanagi result. This extends previous holographic checks on the island rule to non-asymptotic regimes of application, as well as provides a Wald entropy interpretation for $T\\bar T$ entanglement. Finally, we relate our effective theory and its higher derivative corrections to AdS$_3$ gravity with a fluctuating radial cutoff by explicit calculation of the on-shell action.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30533",
  "author_total": 2,
  "authors": [
    {
      "name": "Nele Callebaut"
    },
    {
      "name": "Matteo Selle"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2cbmx6y5dfhbp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30533",
  "fulltext_url": null,
  "id": "2cbmx6y5dfhbp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30533",
  "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"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7204968075",
  "pdf_url": "https://arxiv.org/pdf/2608.30533",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2cbmx6y5dfhbp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2608.30533",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30533"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Brane effective actions and their island rule from $T\\overline T$ flows",
  "title_text": "Brane effective actions and their island rule from TT̅ flows",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/2cbmx6y5dfhbp",
  "venue": "arXiv",
  "versions": []
}