The Conserved Charges and Integrability of the Conformal Affine Toda Models

TL;DR

This paper constructs infinite sets of conserved charges for the conformal affine Toda model, demonstrating their algebraic properties and involution, thereby establishing integrability and connecting to other Toda models.

Contribution

It introduces a novel method to derive conserved charges via abelianization, revealing their chiral nature and Poisson commutation properties in the conformal affine Toda model.

Findings

Infinite sets of conserved charges constructed

Charges of different chiralities Poisson commute

Conserved charges are in involution, confirming integrability

Abstract

We construct infinite sets of local conserved charges for the conformal affine Toda model. The technique involves the abelianization of the two-dimensional gauge potentials satisfying the zero-curvature form of the equations of motion. We find two infinite sets of chiral charges and apart from two lowest spin charges all the remaining ones do not possess chiral densities. Charges of different chiralities Poisson commute among themselves. We discuss the algebraic properties of these charges and use the fundamental Poisson bracket relation to show that the charges conserved in time are in involution. Connections to other Toda models are established by taking particular limits.