{
  "abstract": "We construct Casimir operators of $4D, \\,\\mathcal{N}=2$ supersymmetry algebra in the harmonic superspace approach, and provide the explicit expressions for them in terms of covariant derivatives in the analytic basis. Specifically, the superisospin operator $C_I$ is expressed in terms of new 'long' harmonic derivatives $\\nabla^{\\pm\\pm}, \\nabla^0$ as $C_I = \\frac{1}{4}\\left(\\nabla^0\\right)^2 + \\frac{1}{2}\\left\\{\\nabla^{++},\\nabla^{--}\\right\\}$. These derivatives involve non-local terms with the inverse Box operator $\\Box^{-1}$ and satisfy modified $SU(2)$ algebra relations in which the eigenvalues of $\\nabla^0$ on analytic superfields are shifted by -2 relative to the standard $U(1)$ harmonic charges. We also construct $\\mathcal{N}=2$ superhelicity and super-isohelicity operators relevant to the massless case (with vanishing $\\Box$) and find their eigenvalues for few instructive examples of $4D, \\,\\mathcal{N}=2$ superfield theories.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27412",
  "author_total": 2,
  "authors": [
    {
      "name": "Egor Eremeev"
    },
    {
      "name": "Evgeny Ivanov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5y0c141s406v1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27412",
  "fulltext_url": null,
  "id": "5y0c141s406v1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27412",
  "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"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7204532814",
  "pdf_url": "https://arxiv.org/pdf/2608.27412",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5y0c141s406v1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:26Z",
      "native_id": "2608.27412",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27412"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Casimir operators of $4D\\,, \\mathcal{N}=2$ supersymmetry in the harmonic approach",
  "title_text": "Casimir operators of 4D , 𝒩=2 supersymmetry in the harmonic approach",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/5y0c141s406v1",
  "venue": "arXiv",
  "versions": []
}