{
  "abstract": "Einstein gravity in four asymptotically flat dimensions is governed by a tower of soft theorems obeying an $\\mathcal{L}w_{1+\\infty}$ commutator algebra. This algebra is deformed to $\\mathcal{L}_Λw_{1+\\infty}$ in the conformally related AdS$_4$ and dS$_4$ spacetimes. Here we construct the larger ``conformal $w$-algebra\", denoted $\\mathcal{C}w_{1+\\infty}$, which acts on conformal gravity in all of these spacetimes. It includes $\\mathcal{L}w_{1+\\infty}$, $\\mathcal{L}_Λw_{1+\\infty}$ and the $\\mathfrak{so}(4,2)$ 4D conformal algebra as subalgebras. We show that $\\mathcal{C}w_{1+\\infty}$ is the conformal completion of either $\\mathcal{L}w_{1+\\infty}$ or $\\mathcal{L}_Λw_{1+\\infty}$. A derivation of $\\mathcal{C}w_{1+\\infty}$ is given as the symmetry of the twistor action of self-dual conformal gravity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13381",
  "author_total": 3,
  "authors": [
    {
      "name": "Simon Heuveline"
    },
    {
      "name": "Nia Robles Del Pino"
    },
    {
      "name": "Andrew Strominger"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6c8svkh9797p3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13381",
  "fulltext_url": null,
  "id": "6c8svkh9797p3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13381",
  "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",
      "gr-qc"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7213351527",
  "pdf_url": "https://arxiv.org/pdf/2609.13381",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6c8svkh9797p3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.13381",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13381"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "The Conformal $w$-Algebra",
  "title_text": "The Conformal w-Algebra",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:25Z",
  "url": "https://research.draconitic.com/paper/6c8svkh9797p3",
  "venue": "arXiv",
  "versions": []
}