Noncommutative Instantons on R^2_{NC} x R^2_C

TL;DR

This paper investigates noncommutative instantons on a specific space, demonstrating that singularities are physically irrelevant and that the instanton number remains an integer, thus ensuring regular solutions.

Contribution

It shows that noncommutative instantons on R^2_{NC} x R^2_C are physically regular despite singularities, with instanton number remaining integral, using the ADHM construction.

Findings

Singularities in solutions are gauge-invariant and physically removable.

Instanton number is confirmed to be an integer.

Regular solutions are achievable without involving projected states.

Abstract

We study U(1) and U(2) noncommutative instantons on R^2_{NC} x R^2_C based on the ADHM construction. It is shown that a mild singularity in the instanton solutions for both self-dual and anti-self-dual gauge fields always disappears in gauge invariant quantities and thus physically regular solutions can be constructed even though any projected states are not involved in the ADHM construction. Furthermore the instanton number is also an integer.