  The interplay of gauge dynamics and flavor symmetries often leads to
remarkably subtle phenomena in the presence of soliton configurations.
Non-Abelian vortices -- vortex solutions with continuous internal orientational
moduli -- provide an example. Here we study the effect of weakly gauging a
U(1)_R subgroup of the flavor symmetry on such BPS vortex solutions. Our
prototypical setting consists of an SU(2) x U(1) gauge theory with N_f=2 sets
of fundamental scalars that break the gauge symmetry to an "electromagnetic"
U(1). The weak U(1)_R gauging converts the well-known CP1 orientation modulus
|B| of the non-Abelian vortex into a parameter characterizing the strength of
the magnetic field that is responsible for the Aharonov-Bohm effect. As the
phase of B remains a genuine zero mode while the electromagnetic gauge symmetry
is Higgsed in the interior of the vortex, these solutions are superconducting
strings.
