  Quark confinement is proposed to be a dual Meissner effect of nonAbelian
kind. Important hints come from physics of strongly-coupled
infrared-fixed-point theories in N=2 supersymmetric QCD, which turn into
confining vacua under a small relevant perturbation. The quest for the
semiclassical origin of the nonAbelian monopoles, ubiquitous as the infrared
degrees of freedom in supersymmetric gauge theories, motivates us to study the
quantum dynamics of 2D CP(N-1)model defined on a finite-width worldstrip, with
various boundary conditions. The model is found to possess a unique phase
("confinement phase"), independent of the length of the string, showing the
quantum persistence of the nonAbelian monopole.
