{
  "abstract": "We study the free field realization of the $\\mathcal{W}$-algebra associated with the exceptional Lie algebras $E_6$, $E_7$, $E_8$, and $F_4$. We develop a recursive construction in which a $\\mathcal{W}$-algebra of rank $r$ is obtained from a $\\mathcal{W}$-algebra of rank $r-1$ together with a free boson. The $\\mathcal{W}$-currents are constructed from the zero commutation relation with the screening charges. The $\\mathcal{W}E_6/\\mathcal{W}E_7$ algebra is constructed from the $\\mathcal{W}D_5/\\mathcal{W}D_6$ algebra and is shown to be the same as that realized from the $\\mathcal{W}A_5/\\mathcal{W}E_6$ algebra, up to a change of the free field basis. The spin-$8$ generator of the $\\mathcal{W}E_8$ algebra is built from the $\\mathcal{W}D_7$ algebra. The recursive construction of the $\\mathcal{W}BC_r$ algebras is also studied. We then realize the $\\mathcal{W}F_4$ algebra based on the $\\mathcal{W}BC_3$ algebra. Furthermore, the $\\mathcal{W}$-charges of the generators of the $\\mathcal{W}E_{6,7}$, $\\mathcal{W}BC_{2,3}$, and $\\mathcal{W}F_4$ algebras are calculated and expressed in terms of the Casimir invariants.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14345",
  "author_total": 3,
  "authors": [
    {
      "name": "Daichi Ide"
    },
    {
      "name": "Katsushi Ito"
    },
    {
      "name": "Shigeki Miyazaki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dhr88t2v7pcqp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14345",
  "fulltext_url": null,
  "id": "dhr88t2v7pcqp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14345",
  "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",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7213277181",
  "pdf_url": "https://arxiv.org/pdf/2609.14345",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dhr88t2v7pcqp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:03Z",
      "native_id": "2609.14345",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14345"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Free Field Realization of $\\mathcal{W}$-Algebra Associated with Exceptional Lie Algebras",
  "title_text": "Free Field Realization of 𝒲-Algebra Associated with Exceptional Lie Algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:03Z",
  "url": "https://research.draconitic.com/paper/dhr88t2v7pcqp",
  "venue": "arXiv",
  "versions": []
}