{
  "abstract": "Fuzzy sphere Hamiltonians for (2+1)D conformal field theories are usually written directly on the lowest Landau level. We introduce a framework organizing them as descendants of local ``mother theories'' on $S^2\\times\\mathbb R$. We start with the example of Ising mother theory built from two charged Dirac fermions coupled to a real mediator $ϕ$. Integrating out $ϕ$ and the higher Landau levels produces the fuzzy Hamiltonian, while integrating out the fermions gives a conventional local $ϕ$ effective field theory flowing to the Ising point. Mild modifications of the same theory reach the Gaussian point (tricritical route) and the Lee-Yang continuation. Exploring the space of mother theories, we next promote $ϕ$ to a complex field $Φ$ and construct a new example, whose descendant is an easy-plane ferromagnet on the fuzzy sphere. Its spontaneous symmetry breaking phase gives a pseudo-Goldstone relativistic scalar, similar to the model introduced by Y.-C. He, while its critical point is non-relativistic, providing the first example of $z=2$ scaling on the fuzzy sphere. Remarkably, it admits exact one-magnon solutions, and the $z=2$ critical point can be found analytically. We then outline a rich landscape of further applications of our approach.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38702",
  "author_total": 1,
  "authors": [
    {
      "name": "Mykola Dedushenko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b6yxvfbdn35sr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38702",
  "fulltext_url": null,
  "id": "b6yxvfbdn35sr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38702",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "hep-lat"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38702",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b6yxvfbdn35sr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.38702",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38702"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-lat",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "The Effective Field Theory Origin of the Fuzzy Sphere Method",
  "title_text": "The Effective Field Theory Origin of the Fuzzy Sphere Method",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/b6yxvfbdn35sr",
  "venue": "arXiv",
  "versions": []
}