Novikov-Veselov Symmetries of the Two-Dimensional $O(N)$ Sigma Model

Symmetry Integrability and Geometry-Methods and Applications

article

Igor Krichever¹  Nikita Nekrasov⁴ 

[1] Department of Mathematics, Columbia University;Center for Advanced Studies;Higher School of Economics;Simons Center for Geometry and Physics, Stony Brook University;Kharkevich Institute for Information Transmission Problems

关键词: Novikov-Veselov hierarchy;    sigma model;    Fermi spectral curve.;   

DOI  :  10.3842/SIGMA.2022.006

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown