PreprintOn the classical equivalence of monodromy matrices in squashed sigma modelIo Kawaguchi, Takuya Matsumoto, Kentaroh YoshidaAbstractWe proceed to study the hybrid integrable structure in twodimensional nonlinear sigma models with target space threedimensional squashed spheres. A quantum affine algebra and a pair of Yangian algebras are realized in the sigma models and, according to them, there are two descriptions to describe the classical dynamics 1) the trigonometric description and 2) the rational description, respectively. For every description, a Lax pair is constructed and the associated monodromy matrix is also constructed. In this paper we show the gaugeequivalence of the monodromy matrices in the trigonometric and rational description under a certain relation between spectral parameters and the rescalings of sl(2) generators. Keywords: nonlinear sigma model, Lax pair, monodromy matrix, Yangian algebra, quantum affine algebra.
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