Topological Charge of ADHM Instanton on R^2_{NC}*R^2

TL;DR

This paper confirms that the topological charge of U(N) instantons on degenerate noncommutative space-time equals the instanton number, extending previous results to this specific case.

Contribution

It extends the calculation of topological charge to degenerate noncommutative space-time, confirming it remains equal to the instanton number in this scenario.

Findings

Topological charge equals the instanton number k.

Results hold for degenerate noncommutative space-time.

Completes the understanding of topological charge in noncommutative instantons.

Abstract

We have calculated the topological charge of U(N) instantons on non-degenerate noncommutative space time to be exactly the instanton number k in a previous paper [Mod.Phys.Lett. A18 1691]. This paper, which deals with the degenerate R^2_{NC}*R^2 case, is the continuation of that one. We find that the same conclusion holds in this case, thus complete the answer to the problem of topological charge of noncommutative U(N) instantons.