Sigma models from Gaudin spin chains
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912726823993344 |
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| author | Bykov, Dmitri Kuzovchikov, Andrew |
| author_facet | Bykov, Dmitri Kuzovchikov, Andrew |
| contents | We solve the classical and quantum problems for the 1D sigma model with target space the flag manifold $\mathrm{U}(3)\over \mathrm{U}(1)^3$, equipped with the most general invariant metric. In particular, we explicitly describe all geodesics in terms of elliptic functions and demonstrate that the spectrum of the Laplace-Beltrami operator may be found by solving polynomial (Bethe) equations. The main technical tool that we use is a mapping between the sigma model and a Gaudin model, which is also shown to hold in the $\mathrm{U}(n)$ case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_20889 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sigma models from Gaudin spin chains Bykov, Dmitri Kuzovchikov, Andrew High Energy Physics - Theory Mathematical Physics Differential Geometry Representation Theory We solve the classical and quantum problems for the 1D sigma model with target space the flag manifold $\mathrm{U}(3)\over \mathrm{U}(1)^3$, equipped with the most general invariant metric. In particular, we explicitly describe all geodesics in terms of elliptic functions and demonstrate that the spectrum of the Laplace-Beltrami operator may be found by solving polynomial (Bethe) equations. The main technical tool that we use is a mapping between the sigma model and a Gaudin model, which is also shown to hold in the $\mathrm{U}(n)$ case. |
| title | Sigma models from Gaudin spin chains |
| topic | High Energy Physics - Theory Mathematical Physics Differential Geometry Representation Theory |
| url | https://arxiv.org/abs/2508.20889 |