On the Stability of Non-Abelian Semi-local Vortices

We study the stability of non-Abelian semi-local vortices based on an N = 2 supersymmetric H = SU(Nc)×U(1)/ZNc ∼ U(Nc) gauge theory with an arbitrary number of flavors (Nf > Nc) in the fundamental representation, when certain N = 1 mass terms are present, making the vortex solutions no longer BPS-saturated. Local (ANO-like) vortices are found to be stable against fluctuations in the transverse directions. Strong evidence is found that the ANO-like vortices are actually the true minima. In other words, the semi-local moduli, which are present in the BPS limit, disappear in our non-BPS system, leaving the vortex with the orientational moduli CPNc−1 only. We discuss the implications of this fact on the system in which the U(Nc) model arises as the low-energy approximation of an underlying e.g. G = SU(Nc + 1) gauge theory.