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Novikov–Veselov Symmetries of the Two-Dimensional $O(N)$ Sigma Model
Symmetry, integrability and geometry: methods and applications, Tome 18 (2022) Cet article a éte moissonné depuis la source Math-Net.Ru

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We show that Novikov–Veselov hierarchy provides a complete family of commuting symmetries of two-dimensional $O(N)$ 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.
Keywords: Novikov–Veselov hierarchy, sigma model, Fermi spectral curve. 
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Igor Krichever; Nikita Nekrasov. Novikov–Veselov Symmetries of the Two-Dimensional $O(N)$ Sigma Model. Symmetry, integrability and geometry: methods and applications, Tome 18 (2022). http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a5/

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