{
  "abstract": "We extend the recursive construction of free-field realizations proposed by Ide, Ito, and Miyazaki to the $\\mathcal{N} = 1$ supersymmetric $\\mathcal{W}$-algebras $\\mathcal{SW} B (n - 1 , n)$ and $\\mathcal{SW} B (n , n)$, associated with the Lie superalgebras $B (n - 1 , n)$ and $B (n , n)$, respectively. We obtain explicit free-field realizations of $\\mathcal{SW} B (0 , 1)$, $\\mathcal{SW} B (1 , 1)$, $\\mathcal{SW} B (1 , 2)$, and $\\mathcal{SW} B (2 , 2)$. In particular, the realizations of $\\mathcal{SW} B (1 , 2)$ and $\\mathcal{SW} B (2 , 2)$ are new. Using these realizations, we compute central charges, conformal weights, and eigenvalues of the generating currents on free-field highest-weight states, and construct the local integrals of motion $I_1$, $I_3$, and $I_5$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27853",
  "author_total": 1,
  "authors": [
    {
      "name": "Naozumi Tanabe"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6znb9cd8sep32.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27853",
  "fulltext_url": null,
  "id": "6znb9cd8sep32",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27853",
  "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"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7223139268",
  "pdf_url": "https://arxiv.org/pdf/2610.27853",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6znb9cd8sep32.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.27853",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27853"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Free-field realizations of $\\mathcal{N} = 1$ supersymmetric $\\mathcal{W}$-algebras associated with Lie superalgebras $B (n - 1 , n)$ and $B (n , n)$",
  "title_text": "Free-field realizations of 𝒩 = 1 supersymmetric 𝒲-algebras associated with Lie superalgebras $B (n - 1 , n)$ and $B (n , n)$",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/6znb9cd8sep32",
  "venue": "arXiv",
  "versions": []
}