{
  "abstract": "A bstract : We develop the theory of the first-order dynamical systems, called the Euclidean ℰ-models, which naturally give rise in their second-order formulation to non-unitary nonlinear σ -models with real Euclidean actions. We establish the Euclidean version of Poisson-Lie T-duality, formulate sufficient conditions for Lax integrability, and describe the one-loop renormalization flow of the Euclidean ℰ-operator.\n\nFor perfect Drinfeld doubles, we introduce the ℰ-Wick rotation, which canonically associates a Euclidean ℰ-model with every Lorentzian one. In the families studied here, this construction induces natural analytic continuations relating the Lorentzian and Euclidean Lax representations and renormalization-group flows, while preserving Poisson-Lie duality.\n\nAs the principal example, we construct the Euclidean bi-Yang-Baxter model on the Lu-Weinstein double and determine explicitly its action, Lax representation, Poisson-Lie dual and one-loop renormalization-group flow. We identify a one-parameter family of one-loop RG fixed points for which the target-space geometry develops singularities on the maximal torus of K , whereas the dual model with target K ℂ /K has an everywhere regular background. This regular dual model turns out to be a one-parameter deformation of the non-unitary hyperbolic Wess-Zumino-Witten model.",
  "abstract_shown": true,
  "affiliations": [
    "Institut de Mathématiques de Marseille, UMR 7373, Aix Marseille Université, CNRS"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Ctirad Klimčík",
      "orcid": "0000-0003-3018-7147"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7539j0cn0ktha.bib",
  "cited_by": 0,
  "doi": "10.1007/jhep10(2026)002",
  "fulltext_url": null,
  "id": "7539j0cn0ktha",
  "issns": [
    "1029-8479"
  ],
  "landing_url": "https://link.springer.com/10.1007/JHEP10(2026)002",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7215092075",
  "pdf_url": "https://link.springer.com/content/pdf/10.1007/JHEP10(2026)002.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": "Springer Science and Business Media LLC",
  "ris": "https://research.draconitic.com/paper/7539j0cn0ktha.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:01Z",
      "native_id": "10.1007/jhep10(2026)002",
      "source": "crossref",
      "url": "https://link.springer.com/10.1007/JHEP10(2026)002"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3106|Black Holes and Theoretical Physics",
      "subfield": "high-energy"
    }
  ],
  "title": "Euclidean ℰ-models",
  "title_text": "Euclidean ℰ-models",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:01Z",
  "url": "https://research.draconitic.com/paper/7539j0cn0ktha",
  "venue": "Journal of High Energy Physics",
  "versions": []
}