Moyal Deformation, Seiberg-Witten-Map, and Integrable Models

TL;DR

This paper develops a covariant framework for Moyal deformations of gauge theories and integrable models, illustrating how Seiberg-Witten maps operate within noncommutative settings, exemplified by a noncommutative principal chiral model.

Contribution

It introduces a covariant formalism for Moyal deformations and analyzes the Seiberg-Witten map's role in noncommutative integrable models, including a specific noncommutative principal chiral model.

Findings

Constructed noncommutative integrable models using Moyal products.

Analyzed the action of Seiberg-Witten maps in noncommutative gauge theories.

Provided a concrete example with a noncommutative principal chiral model.

Abstract

A covariant formalism for Moyal deformations of gauge theory and differential equations which determine Seiberg-Witten maps is presented. Replacing the ordinary product of functions by the noncommutative Moyal product, noncommutative versions of integrable models can be constructed. We explore how a Seiberg-Witten map acts in such a framework. As a specific example, we consider a noncommutative extension of the principal chiral model.