Instantons on General Noncommutative R^4

TL;DR

This paper investigates explicit instanton solutions in U(1) and U(2) gauge theories on general noncommutative R^4, revealing that instanton charges are integer-valued and independent of noncommutative parameters.

Contribution

It provides explicit projection operators for instantons on noncommutative R^4 and demonstrates the charge's independence from noncommutative parameters.

Findings

Instanton charges are integers.

Explicit projection operators are derived.

Charge remains constant across noncommutative parameters.

Abstract

We study the U(1) and U(2) instanton solutions of gauge theory on general noncommutative $\bf{R}^4$. In all cases considered we obtain explicit results for the projection operators. In some cases we computed numerically the instanton charge and found that it is an integer, independent of the noncommutative parameters $\theta_{1,2}$.