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| _version_ | 1862647227077361664 |
|---|---|
| author | Krichever, Igor Nekrasov, Nikita |
| author_facet | Krichever, Igor Nekrasov, Nikita |
| citation_txt | Novikov-Veselov Symmetries of the Two-Dimensional () Sigma Model. Igor Krichever and Nikita Nekrasov. SIGMA 18 (2022), 006, 37 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-15T12:06:12Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211539 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T12:06:12Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Krichever, Igor Nekrasov, Nikita 2026-01-05T12:30:14Z 2022 Novikov-Veselov Symmetries of the Two-Dimensional () Sigma Model. Igor Krichever and Nikita Nekrasov. SIGMA 18 (2022), 006, 37 pages 1815-0659 2020 Mathematics Subject Classification: 14H70; 17B80; 35J10; 37K10; 37K20; 37K30; 81R12 arXiv:2106.14201 https://nasplib.isofts.kiev.ua/handle/123456789/211539 https://doi.org/10.3842/SIGMA.2022.006 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Novikov-Veselov Symmetries of the Two-Dimensional () Sigma Model Article published earlier |
| spellingShingle | Novikov-Veselov Symmetries of the Two-Dimensional () Sigma Model Krichever, Igor Nekrasov, Nikita |
| title | Novikov-Veselov Symmetries of the Two-Dimensional () Sigma Model |
| title_full | Novikov-Veselov Symmetries of the Two-Dimensional () Sigma Model |
| title_fullStr | Novikov-Veselov Symmetries of the Two-Dimensional () Sigma Model |
| title_full_unstemmed | Novikov-Veselov Symmetries of the Two-Dimensional () Sigma Model |
| title_short | Novikov-Veselov Symmetries of the Two-Dimensional () Sigma Model |
| title_sort | novikov-veselov symmetries of the two-dimensional () sigma model |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211539 |
| work_keys_str_mv | AT kricheverigor novikovveselovsymmetriesofthetwodimensionalsigmamodel AT nekrasovnikita novikovveselovsymmetriesofthetwodimensionalsigmamodel |