Local conserved charges in principal chiral models

TL;DR

This paper investigates local conserved charges in 1+1 dimensional principal chiral models, demonstrating their involution with non-local charges and constructing an infinite set of commuting local charges related to the algebra's exponents.

Contribution

It constructs an infinite set of local conserved charges in principal chiral models and analyzes their algebraic properties, including involution and commutation relations.

Findings

Local conserved charges exist for each symmetric invariant tensor.

These charges are in involution with non-local Yangian charges.

An infinite set of commuting local charges is constructed for each classical algebra.

Abstract

Local conserved charges in principal chiral models in 1+1 dimensions are investigated. There is a classically conserved local charge for each totally symmetric invariant tensor of the underlying group. These local charges are shown to be in involution with the non-local Yangian charges. The Poisson bracket algebra of the local charges is then studied. For each classical algebra, an infinite set of local charges with spins equal to the exponents modulo the Coxeter number is constructed, and it is shown that these commute with one another. Brief comments are made on the evidence for, and implications of, survival of these charges in the quantum theory.