On the classical equivalence of monodromy matrices in squashed sigma model

TL;DR

This paper demonstrates the gauge-equivalence of monodromy matrices in two different algebraic descriptions of the squashed sigma model, revealing a classical equivalence between trigonometric and rational formulations.

Contribution

It establishes the classical gauge-equivalence of monodromy matrices in the trigonometric and rational descriptions of the integrable structure in the squashed sigma model.

Findings

Monodromy matrices in both descriptions are gauge-equivalent.

A specific relation between spectral parameters links the two descriptions.

The equivalence is shown under rescaling of sl(2) generators.

Abstract

We proceed to study the hybrid integrable structure in two-dimensional non-linear sigma models with target space three-dimensional 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 gauge-equivalence of the monodromy matrices in the trigonometric and rational description under a certain relation between spectral parameters and the rescalings of sl(2) generators.