Hidden Yangian symmetry in sigma model on squashed sphere

TL;DR

This paper reveals a hidden Yangian symmetry in a sigma model on a squashed sphere, demonstrating an infinite set of conserved charges and algebraic structure, with implications for warped AdS_3 spaces.

Contribution

It uncovers a Yangian symmetry in the sigma model on a squashed sphere and connects it to the coset structure and warped AdS_3 spaces.

Findings

Existence of an infinite number of conserved non-local charges.

Yangian algebra verified through Serre relations.

Symmetry extends to warped AdS_3 spaces via double Wick rotations.

Abstract

We discuss a hidden symmetry of a two-dimensional sigma model on a squashed S^3. The SU(2) current can be improved so that it can be regarded as a flat connection. Then we can obtain an infinite number of conserved non-local charges and show the Yangian algebra by directly checking the Serre relation. This symmetry is also deduced from the coset structure of the squashed sphere. The same argument is applicable to the warped AdS_3 spaces via double Wick rotations.