  Recently a low-energy effective theory on non-Abelian semilocal vortices in
SQCD with the U(N) gauge group and N + \tilde{N} quark flavors was obtained in
field theory arXiv:1104.2077. The result is exact in a certain limit of large
infrared cut-off. The resulting model was called the zn model. We study quantum
dynamics of the zn model in some detail. First we solve it at large N in the
leading order. Then we compare our results with those of Hanany and Tong
hep-th/0403158 (the HT model) who based their derivation on a certain type-IIA
formalism, rather than on a field-theory construction. In the 't Hooft limit of
infinite N both model's predictions are identical. At finite N our calculations
agree with the Hanany-Tong results only in the BPS sector. Beyond the BPS
sector there is no agreement between the zn and HT models. Finally, we study
perturbation theory of the zn model from various standpoints.
