Hybrid classical integrability in squashed sigma models

TL;DR

This paper demonstrates the realization of Yangian and q-deformed SU(2) symmetries in a squashed sphere sigma model, developing dual rational and trigonometric descriptions of its classical integrability.

Contribution

It introduces dual descriptions of classical integrability in a squashed sphere sigma model based on different symmetry realizations, linked by a non-local map.

Findings

Yangian and q-deformed SU(2) symmetries are realized in the model.

Two equivalent descriptions of classical dynamics are developed: rational and trigonometric.

Both descriptions lead to the same equations of motion via different Lax pairs.

Abstract

We show that SU(2)_L Yangian and q-deformed SU(2)_R symmetries are realized in a two-dimensional sigma model defined on a three-dimensional squashed sphere. These symmetries enable us to develop the two descriptions to describe its classical dynamics, 1) rational and 2) trigonometric descriptions. The former 1) is based on the SU(2)_L symmetry and the latter 2) comes from the broken SU(2)_R symmetry. Each of the Lax pairs constructed in both ways leads to the same equations of motion. The two descriptions are related one another through a non-local map.