{
  "abstract": "We investigate the reconstruction of the first-order gravitational action from the Noether identities associated with diffeomorphism invariance. The independent fields are a symmetric perturbation $ϕ^{μν}$ of the contravariant metric density and a trace-adjusted connection $G^λ{}_{μν}$, whose transformation laws are prescribed. For a local action polynomial in these fields, with the gravitational coupling as its only dimensionful constant and each additional field carrying one power of it, a dilatation, which is a particular diffeomorphism, shows that in any dimension $d>2$ the action terminates at most at cubic order, its only possible cubic term being a derivative-free $ϕGG$ vertex. Expanding the kernels of the resulting Lorentz-covariant ansatz in tensor bases gives 31 coefficients for $d\\geq 4$. The Noether identities with general diffeomorphisms, expanded order by order in the fields, yield a linear system that eliminates the $ϕϕ$ kernel and determines the remaining coefficients up to an overall normalization, recovering the Goldberg-Palatini action. Since the connection can be eliminated exactly, this also fixes the complete second-order action, with its infinite set of graviton vertices. The construction requires no choice of energy-momentum tensor, the source of ambiguity in the self-coupling approach. The kernel bases, the identities and the solution are given in appendices, and the symbolic computations are publicly available.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28065",
  "author_total": 2,
  "authors": [
    {
      "name": "F. T. Brandt"
    },
    {
      "name": "Augusto C. B. Carvalho"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8y7yzkb8nw2xw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28065",
  "fulltext_url": null,
  "id": "8y7yzkb8nw2xw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28065",
  "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",
      "3103|Cosmology and Gravitation Theories"
    ]
  ],
  "openalex": "W7223087549",
  "pdf_url": "https://arxiv.org/pdf/2610.28065",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8y7yzkb8nw2xw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.28065",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28065"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Reconstructing the Goldberg-Palatini Action from Noether Identities",
  "title_text": "Reconstructing the Goldberg-Palatini Action from Noether Identities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:04Z",
  "url": "https://research.draconitic.com/paper/8y7yzkb8nw2xw",
  "venue": "arXiv",
  "versions": []
}