• confinement
• duality
• monopole
• sigma model
• supersymmetry
• vortex

This thesis is to investigate the moduli spaces and the low-energy effective theories of the BPS non-Abelian vortices in supersymmetric gauge theories with $U(1)\times SU(N)$, $U(1)\times SO(2M)$, $U(1) \times SO(2M+1)$ and $U(1)\times
USp(2M)$ gauge groups. The Goddard-Nuyts-Olive-Weinberg (GNOW) dual group emerges from the transformation properties of the vortex solutions under the original, exact global symmetry group acting on the fields of the theory in the color-flavor locking phase.
The moduli spaces of the vortices turn out to
have the structure of those of quantum states, with sub-moduli corresponding to various
irreducible representations of the GNOW dual group of the color-flavor group.
We explicitly construct the vortex effective world-sheet action forvarious groups and winding numbers, representing the long-distance
fluctuations of the non-Abelian orientational moduli parameters. They are found to be two-dimensional sigma models living on appropriate coset spaces, depending on the gauge group, global symmetry, and on the winding number.

The mass-deformed sigma models are then constructed from the vortex solutions in
the corresponding unequal-mass theories, and they are found to agree with the two-dimensional models obtained from the Scherk-Schwarz dimensional reduction. The moduli spaces of higher-winding BPS non-Abelian vortices in $U(N)$ theory are also investigated by using the K\"ahler quotient construction, which clarifies considerably the group-theoretic properties of the multiply-wound
non-Abelian vortices. Certain orbits, corresponding to irreducible representations are identified; they are associated with the corresponding Young tableau.