Euclidean ℰ-models — Draconitic Research

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.

For 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.

As 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.

Cite

BibTeX RIS

BibTeX

@article{klimcik2026euclidean,
  title = {{Euclidean ℰ-models}},
  author = {Ctirad Klimčík},
  journal = {Journal of High Energy Physics},
  year = {2026},
  month = oct,
  doi = {10.1007/jhep10(2026)002},
  url = {https://link.springer.com/10.1007/JHEP10(2026)002},
  note = {CC BY 4.0},
}

RIS

TY  - JOUR
TI  - Euclidean ℰ-models
AU  - Ctirad Klimčík
PY  - 2026
DA  - 2026/10/01
JO  - Journal of High Energy Physics
DO  - 10.1007/jhep10(2026)002
UR  - https://link.springer.com/10.1007/JHEP10(2026)002
AB  - 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.  For 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.  As 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.
SN  - 1029-8479
ER  -