K-VORTEX DYNAMICS IN $\mathcal{N}\, = \,1^*$ THEORY AND IN ITS GRAVITY DUAL.

We study magnetic flux tubes in the Higgs vacuum of the ${\cal N}\, = \,1^*$ mass deformation of SU(N_c), ${\cal N}\, = \,4$ 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_Nc-valued magnetic flux, with topological winding 0 < k < N_c. These k-strings spontaneously break SO(3)_C+F to U(1)_C+F resulting in an S² moduli space of solutions. The world-sheet sigma model is a nonsupersymmetric ℂℙ¹ model with a theta angle θ₁₊₁ = k(N_c - k)θ₃₊₁ where θ₃₊₁ is the Yang-Mills vacuum angle. We find numerically that k-vortex tensions follow the Casimir scaling law T_k ∝ 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 AdS₅ × S⁵ 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 kD-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 ${\cal N}\, = \,1^*$ theory in the large N_c limit. [ABSTRACT FROM AUTHOR]