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

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 $ν$ and the charge m of the monopole that appears in the effective theory. It is given by $ν= m Φ/(2π)$, where $Φ$ is the quantized flux associated with a U(1) gauge field passing through the loop formed by the singularity of the monopole.