Recently, a low-energy effective theory on non-Abelian semilocal vortices in $\mathcal{N}=2$ supersymmetric quantum chromodynamics with the $\mathrm{U}(N)$ gauge group and $N+\tilde{N}$ quark flavors was obtained in field theory [M. Shifman, W. Vinci, and A. Yung, Phys. Rev. D 83, 125017 (2011).]. 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 [A. Hanany and D. Tong, J. High Energy Phys. 04 (2004) 066.] (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.

• Received 26 July 2011

DOI:https://doi.org/10.1103/PhysRevD.84.065018