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≥Nf≥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.
Bibliographical noteFunding Information:
We are grateful to Hitoshi Murayama for discussions on the homotopy group properties of the nonabelian monopoles, and to Adam Ritz for useful conversations. A.Y. would like to thank Istituto Nazionale di Fisica Nucleare, Sezione di Pisa, for hospitality. The work of A.Y. was supported by Russian Foundation for Basic Research under the grant No 02-02-17115 and by INTAS grant No 00-00334. K.K. thanks Japan Society for the Promotion of Science (Fellow ID S-03034) and N. Sakai (Tokyo Institute of Technology) for hospitality.