Comments on Noncommutative ADHM Construction

TL;DR

This paper extends the matrix partition method to explicitly construct gauge fields in noncommutative ADHM theory, providing new explicit solutions for instantons, including the U(2) 2-instanton and 't Hooft instantons.

Contribution

It introduces a generalized matrix partition technique for explicit gauge field construction in noncommutative ADHM, applicable to various instanton configurations.

Findings

Explicit gauge fields for U(2) 2-instanton in the coincident limit

Application of the method to noncommutative 't Hooft instantons

Simplified derivation of instanton solutions in noncommutative space

Abstract

We extend the method of matrix partition to obtain explicitly the gauge field for noncommutative ADHM construction in some general cases. As an application of this method we apply it to the U(2) 2-instanton and get explicit result for the gauge fields in the coincident instanton limit. We also easily apply it to the noncommutative 't Hooft instantons in the appendix.