Quantum, higher-spin, local charges in symmetric space sigma models

TL;DR

This paper investigates the existence of quantum local conserved charges in two-dimensional symmetric space sigma models, establishing their connection with non-local Yangian charges and analyzing potential anomalies.

Contribution

It demonstrates that quantum local conserved charges exist precisely in models with quantum non-local Yangian charges, linking classical symmetries to quantum integrability.

Findings

Quantum local charges are present in models with Yangian symmetry.

Potential anomalies are analyzed for spin-3 and spin-4 currents.

Consistency with S-matrix results and Yangian representations is confirmed.

Abstract

Potential anomalies are analysed for the local spin-3 and spin-4 classically conserved currents in any two-dimensional sigma model on a compact symmetric space $G/H$, with $G$ and $H$ classical groups. Quantum local conserved charges are shown to exist in exactly those models which also possess quantum non-local (Yangian) charges. The possibility of larger sets of quantum local charges is discussed and shown to be consistent with known S-matrix results and the behaviour of the corresponding Yangian representations.