Instantons, monopoles and the flux quantization in the Faddeev-Niemi decomposition

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 instan ton number nu and the charge m of the monopole that appears in the effectiv e theory. It is given by nu = m Phi>(*) over bar * (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. (C) 2000 Elsevier Science B.V. All rights reserved.