The classical origin of quantum affine algebra in squashed sigma models

Abstract

We consider a quantum affine algebra realized in two-dimensional non-linear sigma models with target space three-dimensional squashed sphere. Its affine generators are explicitly constructed and the Poisson brackets are computed. The defining relations of quantum affine algebra in the sense of the Drinfeld first realization are satisfied at classical level. The relation to the Drinfeld second realization is also discussed including higher conserved charges. Finally we comment on a semiclassical limit of quantum affine algebra at quantum level.