{
  "abstract": "We ask when tree-level supersymmetric cohomology admits a Hironaka decomposition: a unique expansion in finitely many secondary operators with polynomial coefficients in algebraically independent bosonic primaries. Such a decomposition organizes the cohomology into towers with a common set of unrestricted dressings. For diagonal models with $N$ labels, $d\\geq1$ bosonic species and $f$ fermionic species, we construct this decomposition and obtain $(N!)^{d-1}2^{fN}$ secondaries. We also prove that the scalar-branch ring of ABJM theory admits a Hironaka decomposition at every rank and positive integer Chern--Simons level, and construct explicit bases for the $SU(2)\\times SU(2)$ Klebanov--Witten scalar ring. We also do the same for the Higgs branches of two class-S theories. However, not all supersymmetric cohomologies admit a Hironaka decomposition. In the Wess--Zumino model with $W=x^2y^2$, every positive-degree scalar annihilates the nonzero class $xy$, while $x^n$ is in cohomology for every $n\\geq 1$. These two properties rule out a Hironaka decomposition over scalar primaries.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36094",
  "author_total": 3,
  "authors": [
    {
      "name": "Abhijit Gadde"
    },
    {
      "name": "Rajat Raj"
    },
    {
      "name": "Shivansh Tomar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4zky6gnfxk1np.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36094",
  "fulltext_url": null,
  "id": "4zky6gnfxk1np",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36094",
  "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": "W7224120557",
  "pdf_url": "https://arxiv.org/pdf/2610.36094",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4zky6gnfxk1np.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2610.36094",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36094"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Hironaka decompositions in supersymmetric theories: an exploration",
  "title_text": "Hironaka decompositions in supersymmetric theories: an exploration",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:50Z",
  "url": "https://research.draconitic.com/paper/4zky6gnfxk1np",
  "venue": "arXiv",
  "versions": []
}