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 c...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2022 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2022
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| Online Zugang: | 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 |
| Zitieren: | Novikov-Veselov Symmetries of the Two-Dimensional ( ) Sigma Model. Igor Krichever and Nikita Nekrasov. SIGMA 18 (2022), 006, 37 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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 |