Instantons, Monopoles and the Flux Quantization in the Faddeev-Niemi Decomposition

TL;DR

This paper explores the emergence of instantons in the low energy effective theory of SU(2) Yang-Mills, revealing a relation between instanton number and monopole charge linked through flux quantization.

Contribution

It establishes a simple relation between instanton number and monopole charge in the Faddeev-Niemi decomposition of Yang-Mills theory.

Findings

Instantons are related to monopole charges via flux quantization.

A formula connecting instanton number and monopole charge is derived.

The flux associated with monopoles is quantized and influences instanton properties.

Abstract

We study how instantons arise in the low energy effective theory of the SU(2) Yang-Mills theory in the context of the non-linear sigma model recently propose by Faddeev and Niemi. We find a simple relation between the instanton number $\nu$ and the charge m of the monopole that appears in the effective theory. It is given by $\nu = m \Phi/(2\pi)$, where $\Phi$ is the quantized flux associated with a U(1) gauge field passing through the loop formed by the singularity of the monopole.