The classical origin of quantum affine algebra in squashed sigma models

TL;DR

This paper demonstrates how quantum affine algebra arises in two-dimensional squashed sigma models, explicitly constructing its generators, verifying algebraic relations, and discussing classical and semiclassical limits.

Contribution

It provides the first explicit construction of quantum affine algebra in squashed sigma models and explores its classical and quantum relations.

Findings

Affine generators are explicitly constructed.

Poisson brackets satisfy quantum affine algebra relations.

Relation to Drinfeld second realization and semiclassical limit discussed.

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.