{
  "abstract": "This paper is a third one in a series devoted to the construction of $2D$, $\\mathbb{Z}_2^2$-graded, integrable Toda field theories. The first paper introduced parabosonic models obtained from Rittenberg-Wyler color Lie algebras; the second paper explained how to deal with parafermions (the $\\mathbb{Z}_2^2$-graded super-Liouville theory) from finite Rittenberg-Wyler color Lie superalgebras. This new paper extends the construction to the infinite case of (twisted) affine color Lie superalgebras. A $\\mathbb{Z}_2^2$-graded extension of ${\\widehat{\\mathfrak{osp}(2|2)^{(2)}}}$ allows to interpolate the super-Liouville and the super-Sinh-Gordon models, recovered as special limits. The $\\mathbb{Z}_2^2$-graded extensions of three frameworks are here discussed: the Polyakov's soldering, the Leznov-Savel'ev Lax pair (zero-curvature) formulation and the Bäcklund transformations. As a byproduct of the construction, the Hamiltonian reduction from the $\\mathbb{Z}_2^2$-graded ${\\widehat{\\mathfrak{osp(2|2)}^{(2)}}}$ WZNW models induces a $\\mathbb{Z}_2^2$-graded color Lie superalgebra which admits three inequivalent superVirasoro subalgebras; they are the ${\\cal N}=2$ superVirasoro, the $(1,\\frac{3}{2},\\frac{3}{2},2)$ $\\mathbb{Z}_2^2$-graded superVirasoro and the $(\\frac{3}{2},\\frac{3}{2},2,2)$ $\\mathbb{Z}_2^2$-graded superVirasoro.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33485",
  "author_total": 4,
  "authors": [
    {
      "name": "Naruhiko Aizawa"
    },
    {
      "name": "Ren Ito"
    },
    {
      "name": "Luiza Miranda"
    },
    {
      "name": "Francesco Toppan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3nqhnjhjfcdvr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33485",
  "fulltext_url": null,
  "id": "3nqhnjhjfcdvr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33485",
  "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",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7223914225",
  "pdf_url": "https://arxiv.org/pdf/2610.33485",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3nqhnjhjfcdvr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.33485",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33485"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "A Twisted Affine Interpolation of the $\\mathbb{Z}_2^2$-graded Integrable Super-Liouville and super-Sinh-Gordon Equations",
  "title_text": "A Twisted Affine Interpolation of the ℤ_2^2-graded Integrable Super-Liouville and super-Sinh-Gordon Equations",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/3nqhnjhjfcdvr",
  "venue": "arXiv",
  "versions": []
}