Conserved Charges in the Principal Chiral Model on a Supergroup

TL;DR

This paper explores the classical principal chiral model on a Lie supergroup, demonstrating the construction of local conserved charges, their algebraic properties, and their relation to non-local charges, advancing understanding of integrability in supersymmetric models.

Contribution

It introduces a method to construct local conserved charges in the supergroup principal chiral model and analyzes their algebraic structure and relation to non-local charges.

Findings

Constructed local conserved charges from invariant tensors.

Calculated super-Poisson brackets showing finite generation.

Proved charges commute with non-local charges.

Abstract

The classical principal chiral model in 1+1 dimensions with target space a compact Lie supergroup is investigated. It is shown how to construct a local conserved charge given an invariant tensor of the Lie superalgebra. We calculate the super-Poisson brackets of these currents and argue that they are finitely generated. We show how to derive an infinite number of local charges in involution. We demonstrate that these charges Poisson commute with the non-local charges of the model.