Instantons, monopoles and the flux quantization in the Faddeev–Niemi decomposition Original Research Article

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 proposed 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=mΦ/(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.