{
  "abstract": "We revisit Deser's current reconstruction in first-order Yang--Mills theory with an independent two-form. We fix the quadratic auxiliary sector and the first gauge correction, and ask whether a prescribed curvature interaction can be added without higher-order action terms. For a compact semisimple gauge algebra, requiring the mixed Noether identity to close without a $gh$ action term fixes the algebraic auxiliary representative to the tangent representative, up to linear curvature and dual-curvature terms on each simple ideal. For the analytic radial class $U=Φ(f\\cdot f)$, with first nonlinear term $c_p(f\\cdot f)^p$, no allowed representative avoids a third-order action correction when all second-order action coefficients vanish. A free-field scaling argument inside a root $\\mathfrak{su}(2)$ subalgebra establishes this result for every compact semisimple gauge algebra. Ordinary covariantization and an auxiliary-field shift give an explicit completion. For $p=2$, its seven-gluon contact term cancels a nonzero tree-level Ward contraction at real nonsingular kinematics. We also study an affine star-gauge sector motivated by Seiberg--Witten maps, where strict current feedback and second-order action truncation select different representatives. Together these results show how the prescribed auxiliary data determine which interactions are required by current reconstruction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19402",
  "author_total": 1,
  "authors": [
    {
      "name": "Carolina Matté Gregory"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cvempsa1vzknt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19402",
  "fulltext_url": null,
  "id": "cvempsa1vzknt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19402",
  "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",
      "hep-th"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.19402",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cvempsa1vzknt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2609.19402",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19402"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Current Reconstruction and Higher Interactions in Gauge Theory",
  "title_text": "Current Reconstruction and Higher Interactions in Gauge Theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:19Z",
  "url": "https://research.draconitic.com/paper/cvempsa1vzknt",
  "venue": "arXiv",
  "versions": []
}