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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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2022
ISSN:1815-0659
Main Authors: Krichever, Igor, Nekrasov, Nikita
Format: Article
Language:English
Published: Інститут математики НАН України 2022
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/211539
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Novikov-Veselov Symmetries of the Two-Dimensional () Sigma Model. Igor Krichever and Nikita Nekrasov. SIGMA 18 (2022), 006, 37 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Summary: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.
ISSN:1815-0659