Integrable Higher-Spin Deformations of Sigma Models from Auxiliary Fields
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916357031854080 |
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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 construct a new infinite family of integrable deformations of the principal chiral model (PCM) parameterized by an interaction function of several variables, which extends the formalism of arXiv:2405.05899, and includes deformations of the PCM by functions of both the stress tensor and higher-spin conserved currents. We show in detail that every model in this class admits a Lax representation for its equations of motion, and that the Poisson bracket of the Lax connection takes the Maillet form, establishing the existence of an infinite set of Poisson-commuting conserved charges. We argue that the non-Abelian T-dual of any model in this family is classically integrable, and that T-duality "commutes" with a general deformation in this class, in a sense which we make precise. Finally, we demonstrate that these higher-spin auxiliary field deformations can be extended to accommodate the addition of a Wess-Zumino term, and we exhibit the Lax connection in this case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16338 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Integrable Higher-Spin Deformations of Sigma Models from Auxiliary Fields Bielli, Daniele Ferko, Christian Smith, Liam Tartaglino-Mazzucchelli, Gabriele High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems We construct a new infinite family of integrable deformations of the principal chiral model (PCM) parameterized by an interaction function of several variables, which extends the formalism of arXiv:2405.05899, and includes deformations of the PCM by functions of both the stress tensor and higher-spin conserved currents. We show in detail that every model in this class admits a Lax representation for its equations of motion, and that the Poisson bracket of the Lax connection takes the Maillet form, establishing the existence of an infinite set of Poisson-commuting conserved charges. We argue that the non-Abelian T-dual of any model in this family is classically integrable, and that T-duality "commutes" with a general deformation in this class, in a sense which we make precise. Finally, we demonstrate that these higher-spin auxiliary field deformations can be extended to accommodate the addition of a Wess-Zumino term, and we exhibit the Lax connection in this case. |
| title | Integrable Higher-Spin Deformations of Sigma Models from Auxiliary Fields |
| topic | High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2407.16338 |