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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2603.21355 |
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| _version_ | 1866913135496003584 |
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| author | Klimcik, Ctirad |
| author_facet | Klimcik, Ctirad |
| contents | We study a class of $\mathcal{E}$-models, referred to as Euclidean $\mathcal{E}$-models, in which the operator $\mathcal{E}$ acting on the Drinfeld double squares to minus the identity rather than to the identity. This modification leads to significant structural differences from the standard $\mathcal{E}$-model framework. Most notably, the associated $σ$-models naturally possess Euclidean world-sheets and real Euclidean actions.
Although for some Drinfeld doubles every Lorentzian $\mathcal{E}$-model admits a natural Euclidean counterpart, the duality, integrability, and renormalization properties of Euclidean $\mathcal{E}$-models are not determined by the Lorentzian theory and must be studied separately. We develop the basic formalism, provide the Euclidean version of Poisson--Lie T-duality, formulate the Euclidean analogue of the integrability criterion, and describe the Euclidean one-loop renormalization flow. The general constructions are illustrated by the example of the Euclidean bi-Yang--Baxter deformation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21355 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Euclidean E-models Klimcik, Ctirad High Energy Physics - Theory We study a class of $\mathcal{E}$-models, referred to as Euclidean $\mathcal{E}$-models, in which the operator $\mathcal{E}$ acting on the Drinfeld double squares to minus the identity rather than to the identity. This modification leads to significant structural differences from the standard $\mathcal{E}$-model framework. Most notably, the associated $σ$-models naturally possess Euclidean world-sheets and real Euclidean actions. Although for some Drinfeld doubles every Lorentzian $\mathcal{E}$-model admits a natural Euclidean counterpart, the duality, integrability, and renormalization properties of Euclidean $\mathcal{E}$-models are not determined by the Lorentzian theory and must be studied separately. We develop the basic formalism, provide the Euclidean version of Poisson--Lie T-duality, formulate the Euclidean analogue of the integrability criterion, and describe the Euclidean one-loop renormalization flow. The general constructions are illustrated by the example of the Euclidean bi-Yang--Baxter deformation. |
| title | Euclidean E-models |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2603.21355 |