{
  "abstract": "The $\\mathcal N=1$ superconformal minimal model with $m=12$ and the exceptional modular invariant $(E_6,D_8)$ is the unitary minimal model of the super-$W_3$ algebra. We propose its Landau-Ginzburg description using two real scalar superfields with the cubic superpotential ${\\cal W}=g_1 XY^2/2 + g_2X^3/6$. For $g_1=g_2$, this superpotential is known to describe a product of two $m=3$ $\\mathcal N=1$ superconformal minimal models, which is the $m=10$ model with the $(D_6,E_6)$ modular invariant. The exceptional $m=12$ superconformal minimal model is realized at a different fixed point of the same theory. Testing this Landau-Ginzburg description requires the fusion ring of the minimal model, which we obtain from the modular data of the extended algebra. The fusion ring has a $\\mathbb Z_2$ grading by chiral fermion parity that the ordinary fusion coefficients do not determine. This grading, composed with conjugation, gives the generator of the R-parity $\\mathbb Z_2^{R}$ of the Landau-Ginzburg theory. We then treat the theory with superpotential $\\cal W$ as a Gross-Neveu-Yukawa model in $d=4-ε$ and find a weakly coupled infrared fixed point with $g_1/g_2=3/2+\\mathcal O(ε)$, at which supersymmetry emerges. We also describe the renormalization group flow from this fixed point to the decoupled fixed point with $g_1=g_2$. The operator dimensions at the coupled fixed point, continued to $d=2$, agree approximately with their values in the $m=12$ superconformal minimal model. Finally, we estimate the scaling dimensions in the new interacting $d=3$ $\\mathcal N=1$ superconformal field theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10972",
  "author_total": 4,
  "authors": [
    {
      "name": "Yu Nakayama"
    },
    {
      "name": "Andrei Katsevich"
    },
    {
      "name": "Igor R. Klebanov"
    },
    {
      "name": "Zimo Sun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/47cm41x64qa6q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10972",
  "fulltext_url": null,
  "id": "47cm41x64qa6q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10972",
  "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",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7212312051",
  "pdf_url": "https://arxiv.org/pdf/2609.10972",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/47cm41x64qa6q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.10972",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10972"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Landau-Ginzburg description of an exceptional ${\\mathcal N}=1$ minimal model",
  "title_text": "Landau-Ginzburg description of an exceptional 𝒩=1 minimal model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:12Z",
  "url": "https://research.draconitic.com/paper/47cm41x64qa6q",
  "venue": "arXiv",
  "versions": []
}