Quark confinement via magnetic color-flavor locking

The color-flavor locking phenomenon in the magnetic picture can be the microscopic description of the quark confinement in QCD. We demonstrate it in an N = 2 supersymmetric SU(N-c)(1) x SU(N-c)(2) quiver gauge theory coupled to N-f flavors of quarks (N-f < N-c). This model reduces to SU(N-c)(1+2) gauge theory with N-f flavors when the vacuum expectations value of the link field is much larger than the dynamical scales, and thus provides a continuous deformation of the N = 2 supersymmetric QCD. We study a vacuum which survives upon adding a superpotential term to reduce to N = 1 while preserving the vectorial SU(N-f) flavor symmetry. We find a region of the parameter space where the confinement is described by the Higgsing of a weekly coupled magnetic SU(N-f) x U(1) gauge theory. The Higgsing locks the quantum numbers of SU(N-f) magnetic color to those of SU(N-f) flavor symmetry, and thus the massive magnetic gauge bosons become the singlet and adjoint representations of the flavor group, i.e, the vector mesons. If the qualitative picture remains valid in non-supersymmetric QCD, one can understand the Hidden Local Symmetry as the magnetic dual description of QCD, and the confining string is identified as the vortex of vector meson fields.