Non-Abelian k-Vortex Dynamics in N=1* theory and its Gravity Dual
Abstract
We study magnetic flux tubes in the Higgs vacuum of the N=1* mass deformation of SU(Nc), N=4 SYM and its large Nc string dual, the Polchinski-Strassler geometry. Choosing equal masses for the three adjoint chiral multiplets, for all Nc 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 ZNc-valued magnetic flux, with winding, 0 < k < Nc. 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(Nc-k)θ3+1 where θ3+1 is the Yang-Mills vacuum angle. We find numerically that k-vortex tensions follow the Casimir scaling law Tk k (Nc-k) for large Nc. In the large Nc IIB string dual, the SO(3)C+F symmetry is manifest in the geometry interpolating between AdS5 x 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 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 Nc limit.