Induced charge matching and Wess-Zumino term on quantum modified moduli space

Recently it was proposed that matching of global charges induced in vacuum by slowly varying, topologically non-trivial scalar fields provides consistency conditions analogous to the ’t Hooft anomaly matching conditions. We study matching of induced charges in supersymmetric (Formula presented) gauge theories with quantum modified moduli space. We find that the Wess-Zumino term should be present in the low energy theory in order that these consistency conditions are satisfied. We calculate the lowest homotopy groups of the quantum moduli space, and show that there are no obstructions to the existence of the Wess-Zumino term at arbitrary N. The explicit expression for this term is given. It is shown that neither vortices nor topological solitons exist in the model. The case of softly broken supersymmetry is considered as well. We find that the possibility of the global flavor symmetric vacuum is strongly disfavored.