Auxiliary field sigma models and Yang-Baxter deformations
Abstract We combine the Yang-Baxter (YB) and bi-Yang-Baxter (bi-YB) deformations with higher-spin auxiliary field deformations to construct multi-parameter families of integrable deformations of the principal chiral model on a Lie group G with semi-simple Lie algebra g $$ \mathfrak{g} $$ . In the YB...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-05-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP05(2025)223 |
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| Summary: | Abstract We combine the Yang-Baxter (YB) and bi-Yang-Baxter (bi-YB) deformations with higher-spin auxiliary field deformations to construct multi-parameter families of integrable deformations of the principal chiral model on a Lie group G with semi-simple Lie algebra g $$ \mathfrak{g} $$ . In the YB case, our construction produces one integrable deformation for each pair ( R $$ \mathcal{R} $$ , E), where R $$ \mathcal{R} $$ is an antisymmetric bilinear operator on g $$ \mathfrak{g} $$ obeying the modified classical Yang-Baxter equation and E is a function of several variables. In the bi-YB case, the pair becomes a triplet ( R $$ \mathcal{R} $$ , R ~ $$ \overset{\sim }{\mathcal{R}} $$ , E), where R ~ $$ \overset{\sim }{\mathcal{R}} $$ is another antisymmetric bilinear operator on g $$ \mathfrak{g} $$ obeying the modified classical Yang-Baxter equation. We show that every model in these families is (weakly) classically integrable by exhibiting a Lax representation for their equations of motion. |
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| ISSN: | 1029-8479 |