Commuting charges and symmetric spaces

TL;DR

This paper demonstrates that classical sigma-models with compact symmetric space targets possess infinitely many local, commuting conserved charges, with spins related to the space's exponents and Coxeter number, revealing deep algebraic structures.

Contribution

It provides a closed-form construction of infinitely many conserved charges for sigma-models on compact symmetric spaces with classical groups, linking them to algebraic exponents and Coxeter numbers.

Findings

Existence of infinitely many conserved charges in these models.

Charges are characterized by spins related to the exponents of the symmetric space.

Charges repeat modulo the Coxeter number, indicating underlying algebraic symmetry.

Abstract

Every classical sigma-model with target space a compact symmetric space $G/H$ (with $G$ classical) is shown to possess infinitely many local, commuting, conserved charges which can be written in closed form. The spins of these charges run over a characteristic set of values, playing the role of exponents of $G/H$, and repeating modulo an integer $h$ which plays the role of a Coxeter number.