Homogeneous Yang-Baxter deformations as undeformed yet twisted models
Abstract The homogeneous Yang-Baxter deformation is part of a larger web of integrable deformations and dualities that recently have been studied with motivations in integrable σ-models, solution-generating techniques in supergravity and Double Field Theory, and possible generalisations of the AdS/C...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-04-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP04(2022)053 |
| _version_ | 1797865736253734912 |
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| author | Riccardo Borsato Sibylle Driezen J. Luis Miramontes |
| author_facet | Riccardo Borsato Sibylle Driezen J. Luis Miramontes |
| author_sort | Riccardo Borsato |
| collection | DOAJ |
| description | Abstract The homogeneous Yang-Baxter deformation is part of a larger web of integrable deformations and dualities that recently have been studied with motivations in integrable σ-models, solution-generating techniques in supergravity and Double Field Theory, and possible generalisations of the AdS/CFT correspondence. The σ-models obtained by the homogeneous Yang-Baxter deformation with periodic boundary conditions on the worldsheet are on-shell equivalent to undeformed models, yet with twisted boundary conditions. While this has been known for some time, the expression provided so far for the twist features non-localities (in terms of the degrees of freedom of the deformed model) that prevent practical calculations, and in particular the construction of the classical spectral curve. We solve this problem by rewriting the equation defining the twist in terms of the degrees of freedom of the undeformed yet twisted model, and we show that we are able to solve it in full generality. Remarkably, this solution is a local expression. We discuss the consequences of the twist at the level of the monodromy matrix and of the classical spectral curve, analysing in particular the concrete examples of abelian, almost abelian and Jordanian deformations of the Yang-Baxter class. |
| first_indexed | 2024-04-09T23:14:03Z |
| format | Article |
| id | doaj.art-51de8f80622f419785991e61771e7982 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-09T23:14:03Z |
| publishDate | 2022-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-51de8f80622f419785991e61771e79822023-03-22T10:12:06ZengSpringerOpenJournal of High Energy Physics1029-84792022-04-012022414710.1007/JHEP04(2022)053Homogeneous Yang-Baxter deformations as undeformed yet twisted modelsRiccardo Borsato0Sibylle Driezen1J. Luis Miramontes2Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de Santiago de CompostelaInstituto Galego de Física de Altas Enerxías (IGFAE), Universidade de Santiago de CompostelaInstituto Galego de Física de Altas Enerxías (IGFAE), Universidade de Santiago de CompostelaAbstract The homogeneous Yang-Baxter deformation is part of a larger web of integrable deformations and dualities that recently have been studied with motivations in integrable σ-models, solution-generating techniques in supergravity and Double Field Theory, and possible generalisations of the AdS/CFT correspondence. The σ-models obtained by the homogeneous Yang-Baxter deformation with periodic boundary conditions on the worldsheet are on-shell equivalent to undeformed models, yet with twisted boundary conditions. While this has been known for some time, the expression provided so far for the twist features non-localities (in terms of the degrees of freedom of the deformed model) that prevent practical calculations, and in particular the construction of the classical spectral curve. We solve this problem by rewriting the equation defining the twist in terms of the degrees of freedom of the undeformed yet twisted model, and we show that we are able to solve it in full generality. Remarkably, this solution is a local expression. We discuss the consequences of the twist at the level of the monodromy matrix and of the classical spectral curve, analysing in particular the concrete examples of abelian, almost abelian and Jordanian deformations of the Yang-Baxter class.https://doi.org/10.1007/JHEP04(2022)053Integrable Field TheoriesSigma ModelsAdS-CFT Correspondence |
| spellingShingle | Riccardo Borsato Sibylle Driezen J. Luis Miramontes Homogeneous Yang-Baxter deformations as undeformed yet twisted models Journal of High Energy Physics Integrable Field Theories Sigma Models AdS-CFT Correspondence |
| title | Homogeneous Yang-Baxter deformations as undeformed yet twisted models |
| title_full | Homogeneous Yang-Baxter deformations as undeformed yet twisted models |
| title_fullStr | Homogeneous Yang-Baxter deformations as undeformed yet twisted models |
| title_full_unstemmed | Homogeneous Yang-Baxter deformations as undeformed yet twisted models |
| title_short | Homogeneous Yang-Baxter deformations as undeformed yet twisted models |
| title_sort | homogeneous yang baxter deformations as undeformed yet twisted models |
| topic | Integrable Field Theories Sigma Models AdS-CFT Correspondence |
| url | https://doi.org/10.1007/JHEP04(2022)053 |
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