On the Stability of Non-Abelian Semi-local Vortices

TL;DR

This paper investigates the stability of non-Abelian semi-local vortices in a supersymmetric gauge theory, finding that non-BPS effects eliminate semi-local moduli, leaving only orientational moduli, and establishing the stability of local vortices.

Contribution

It provides the first analysis of semi-local vortex stability in a non-BPS, supersymmetric setting with arbitrary flavors, showing local vortices are the true minima.

Findings

Local vortices are stable against transverse fluctuations.

Semi-local moduli disappear in the non-BPS regime.

Local vortices are the true energy minima.

Abstract

We study the stability of non-Abelian semi-local vortices based on an N=2 supersymmetric H = [SU(Nc) x U(1)]/Z_Nc = 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 CP(Nc-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.