The flux of noncommutative U(1) instanton through the fuzzy spheres

TL;DR

This paper explores the flux of noncommutative U(1) instantons through fuzzy spheres, demonstrating invariance under isometries and independence from sphere radius, using a noncommutative Gauss theorem derived from ADHM construction.

Contribution

It introduces a noncommutative Gauss theorem for U(1) instantons and analyzes their flux invariance and radius independence on fuzzy spheres.

Findings

Flux of U(1) instantons is independent of sphere radius.

Flux remains invariant under isometry transformations.

Established a noncommutative analog of Gauss theorem.

Abstract

From the ADHM construction on noncommutative $R_{\theta}^4$ we investigate different U(1) instanton solutions tied by isometry trasformations. These solutions present a form of vector fields in noncommutative $R_{\theta}^3$ vector space which makes possible the calculus of their fluxes through fuzzy spheres. We establish the noncommutative analog of Gauss theorem from which we show that the flux of the U(1) instantons through fuzzy spheres does not depend on the radius of these spheres and it is invariant under isometry transformations.