Conserved Quantities in Noncommutative Principal Chiral Model with Wess-Zumino Term

TL;DR

This paper develops a noncommutative extension of the U(N) principal chiral model with a Wess-Zumino term, deriving an infinite set of conserved quantities and a Lax formalism to describe the integrable structure.

Contribution

It introduces a noncommutative version of the principal chiral model with Wess-Zumino term and constructs its conserved quantities and Lax formalism, extending integrability methods.

Findings

Constructed noncommutative U(N) principal chiral model with Wess-Zumino term.

Derived infinite local and non-local conserved quantities.

Presented Lax formalism and perturbative equations of motion.

Abstract

We construct noncommutative extension of U(N) principal chiral model with Wess-Zumino term and obtain an infinite set of local and non-local conserved quantities for the model using iterative procedure of Brezin {\it et.al} \cite{BIZZ}. We also present the equivalent description as Lax formalism of the model. We expand the fields perturbatively and derive zeroth- and first-order equations of motion, zero-curvature condition, iteration method, Lax formalism, local and non-local conserved quantities.