Quantum Dynamics of Low-Energy Theory on Semilocal Non-Abelian Strings

TL;DR

This paper investigates the quantum dynamics of the zn model, a low-energy effective theory on non-Abelian semilocal vortices in SQCD, comparing large N and finite N results with the Hanany-Tong model.

Contribution

It provides a detailed quantum analysis of the zn model, including large N solutions and comparison with the Hanany-Tong model, highlighting agreements and discrepancies.

Findings

At large N, zn and HT models agree in predictions.

At finite N, agreement is limited to the BPS sector.

Beyond BPS, the models differ significantly.

Abstract

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.