Auxiliary Field Sigma Models and Yang-Baxter Deformations
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arXiv
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| Format: | Preprint |
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2024
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| author | Bielli, Daniele Ferko, Christian Smith, Liam Tartaglino-Mazzucchelli, Gabriele |
| author_facet | Bielli, Daniele Ferko, Christian Smith, Liam Tartaglino-Mazzucchelli, Gabriele |
| contents | 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 $\mathfrak{g}$. In the YB case, our construction produces one integrable deformation for each pair $(\mathcal{R}, E)$, where $\mathcal{R}$ is an antisymmetric bilinear operator on $\mathfrak{g}$ 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 $(\mathcal{R},\tilde{\mathcal{R}}, E)$, where $\tilde{\mathcal{R}}$ is another antisymmetric bilinear operator on $\mathfrak{g}$ and obeys the non-split inhomogeneous 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09714 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Auxiliary Field Sigma Models and Yang-Baxter Deformations Bielli, Daniele Ferko, Christian Smith, Liam Tartaglino-Mazzucchelli, Gabriele High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems 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 $\mathfrak{g}$. In the YB case, our construction produces one integrable deformation for each pair $(\mathcal{R}, E)$, where $\mathcal{R}$ is an antisymmetric bilinear operator on $\mathfrak{g}$ 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 $(\mathcal{R},\tilde{\mathcal{R}}, E)$, where $\tilde{\mathcal{R}}$ is another antisymmetric bilinear operator on $\mathfrak{g}$ and obeys the non-split inhomogeneous 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. |
| title | Auxiliary Field Sigma Models and Yang-Baxter Deformations |
| topic | High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2408.09714 |