  We study magnetic flux tubes in the Higgs vacuum of the N=1^* mass
deformation of SU(N_c), N=4 SYM and its large N_c string dual, the
Polchinski-Strassler geometry. Choosing equal masses for the three adjoint
chiral multiplets, for all N_c we identify a "colour-flavour locked" symmetry,
SO(3)_{C+F} which leaves the Higgs vacuum invariant. At weak coupling, we find
explicit non-Abelian k-vortex solutions carrying a Z_{N_c}-valued magnetic
flux, with winding, 0 < k < N_c. These k-strings spontaneously break
SO(3)_{C+F} to U(1)_{C+F} resulting in an S^2 moduli space of solutions. The
world-sheet sigma model is a nonsupersymmetric CP^1 model with a theta angle
\theta_{1+1} = k(N_c-k)\theta_{3+1} where \theta_{3+1} is the Yang-Mills vacuum
angle. We find numerically that k-vortex tensions follow the Casimir scaling
law T_k \propto k (N_c-k) for large N_c. In the large N_c IIB string dual, the
SO(3)_{C+F} symmetry is manifest in the geometry interpolating between AdS_5 x
S^5 and the interior metric due to a single D5-brane carrying D3-brane charge.
We identify candidate k-vortices as expanded probe D3-branes formed from a
collection of k D-strings. The resulting k-vortex tension exhibits precise
Casimir scaling, and the effective world-sheet theta angle matches the
semiclassical result. S-duality maps the Higgs to the confining phase so that
confining string tensions at strong 't Hooft coupling also exhibit Casimir
scaling in N=1^* theory in the large N_c limit.
