We study nonabelian vortices (flux tubes) in SU(N) gauge theories, which are responsible for the confinement of (nonabelian) magnetic monopoles. In particular a detailed analysis is given of N = 2 SQCD with gauge group SU(3) deformed by a small adjoint chiral multiplet mass. Tuning the bare quark masses (which we take to be large) to a common value m, we consider a particular vacuum of this theory in which an SU(2) subgroup of the gauge group remains unbroken. We consider 5 ≥ N f ≥ 4 flavors so that the SU(2) sub-sector remains non asymptotically free: the vortices carrying nonabelian fluxes may be reliably studied in a semi-classical regime. We show that the vortices indeed acquire exact zero modes which generate global rotations of the flux in an SU(2) C+F group. We study an effective world sheet theory of these orientational zero modes which reduces to an N = 2 O(3) sigma model in (1+1) dimensions. Mirror symmetry then teaches us that the dual SU(2) group is not dynamically broken.

Non-Abelian magnetic monopoles of Goddard-Nuyts-Olive-Weinberg type have recently been shown to appear as the dominant infrared degrees of freedom in a class of softly broken N = 2 supersymmetric gauge theories in which the gauge group G is broken to various non-Abelian subgroups H by an adjoint Higgs VEV When the low-energy gauge group H is further broken completely by, e.g., squark VEVs, the monopoles representing pi(2)(GIH) are confined by the non-Abelian vortices arising from the breaking of H, discussed recently [hep-th/0307278]. By considering the system with G = SU(N + 1), H =S(U) X U (1)/Z(N), as an example, we show that the total magnetic flux of the minimal monopole agrees precisely with the total magnetic flux flowing along the single minimal vortex. The possibility for such an analysis reflects the presence of free parameters in the theory-the bare quark mass in and the adjoint mass it-such that for m much greater than mu the topologically nontrivial solutions of vortices and of unconfined monopoles exist at distinct energy scales. (C) 2004 Elsevier B.V All rights reserved

Abstract:We analyze the two-dimensional CP N −1 sigma model defined on a finite space interval L, with various boundary conditions, in the large N limit. With the Dirichlet boundary condition at the both ends, we show that the system has a unique phase, which smoothly approaches in the large L limit the standard 2D CP N −1 sigma model in confinement phase, with a constant mass generated for the n i fields. We study the full functional saddle-point equations for finite L, and solve them numerically. The latter reduces to the well-known gap equation in the large L limit. It is found that the solution satisfies actually both the Dirichlet and Neumann conditions.