{
  "abstract": "Courant--Hilbert (CH) deformations unify broad classes of solvable stress-tensor flows including $T\\bar{T}$ and root-$T\\bar{T}$. However, a gravitational action that systematically yields such general deformations has remained unknown. In this Letter, we construct a two-dimensional massive gravity theory whose on-shell action reproduces the complete CH deformation. The gravity sector is defined via an arbitrary function of the eigenvalue ratio $y$ of the relative zweibein. To bypass the technical difficulty of directly eliminating the auxiliary zweibein, we reformulate the matter sector using a $2 \\times 2$ spectral decomposition involving $y$ and a rank-one projector $K$. Sequentially solving the equations of motion---first for $K$ and subsequently for $y$---naturally maps the system onto the Russo-Townsend form of the CH flow. Our work extends Tolley's massive gravity formulation of $T\\bar{T}$ flows to the CH landscape, providing a clear geometric mechanism for solvable stress-tensor flows.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35452",
  "author_total": 4,
  "authors": [
    {
      "name": "Osamu Fukushima"
    },
    {
      "name": "Miyabi Kurihara"
    },
    {
      "name": "Takaki Matsumoto"
    },
    {
      "name": "Kentaroh Yoshida"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5wgekcq0scdj6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35452",
  "fulltext_url": null,
  "id": "5wgekcq0scdj6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35452",
  "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",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7214771262",
  "pdf_url": "https://arxiv.org/pdf/2609.35452",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5wgekcq0scdj6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:32Z",
      "native_id": "2609.35452",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35452"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "A gravitational realization of Courant--Hilbert deformations",
  "title_text": "A gravitational realization of Courant--Hilbert deformations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:28Z",
  "url": "https://research.draconitic.com/paper/5wgekcq0scdj6",
  "venue": "arXiv",
  "versions": []
}