Recently, a low-energy effective theory on non-Abelian semilocal vortices in N=2 supersymmetric quantum chromodynamics with the U(N) gauge group and N+N′ quark flavors was obtained in field theory. The result is exact in a certain limit of large infrared cutoff. 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 (the Hanany-Tong 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 models' predictions are identical. At finite N, our calculations agree with the Hanany-Tong results only in the Bogomol'nyi-Prasad- Sommerfeld monopoles sector. Beyond the Bogomol'nyi-Prasad-Sommerfeld monopoles sector, there is no agreement between the zn and Hanany-Tong models. Finally, we study perturbation theory of the zn model from various standpoints.
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