On the stability of non-Abelian semi-local vortices

Abstract

We study the stability of non-Abelian semi-local vortices based on an N = 2 supersymmetric H = SU ( N c ) × U ( 1 ) / Z N c ∼ U ( N c ) gauge theory with an arbitrary number of flavors ( N f > N c ) 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 C P N c − 1 only. We discuss the implications of this fact on the system in which the U ( N c ) model arises as the low-energy approximation of an underlying e.g. G = SU ( N c + 1 ) gauge theory.