Novikov-Veselov Symmetries of the Two-Dimensional () Sigma Model
We show that the Novikov-Veselov hierarchy provides a complete family of commuting symmetries of the two-dimensional () sigma model. In the first part of the paper, we use these symmetries to prove that the Fermi spectral curve for the double-periodic sigma model is algebraic. Thus, our previous con...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2022 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2022
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211539 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Novikov-Veselov Symmetries of the Two-Dimensional () Sigma Model. Igor Krichever and Nikita Nekrasov. SIGMA 18 (2022), 006, 37 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | We show that the Novikov-Veselov hierarchy provides a complete family of commuting symmetries of the two-dimensional () sigma model. In the first part of the paper, we use these symmetries to prove that the Fermi spectral curve for the double-periodic sigma model is algebraic. Thus, our previous construction of the complexified harmonic maps in the case of irreducible Fermi curves is complete. In the second part of the paper, we generalize our construction to the case of reducible Fermi curves and show that it gives the conformal harmonic maps to even-dimensional spheres. Remarkably, the solutions are parameterized by spectral curves of turning points of the elliptic Calogero-Moser system.
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| ISSN: | 1815-0659 |