| Summary: | We fully investigate the symmetry-breaking patterns occurring upon creation of composite non-Abelian strings: vortex strings in non-Abelian theories where different sets of colors have different amounts of flux. After spontaneous symmetry breaking, there remains some internal color degrees of freedom attached to these objects, which we argue must exist in a flag manifold, a more general kind of projective space than both CP(N) and the Grassmannian manifold. These strings are expected to be Bogomol'nyi-Prasad-Sommerfeld since its constituents are. We demonstrate that this is true and construct a low-energy effective action for the fluctuations of the internal flag moduli, which we then rewrite in two different ways for the dynamics of these degrees of freedom: a gauged linear sigma model with auxiliary fields and a nonlinear sigma model with an explicit target space metric for the flag manifolds, both of which are N=(2,2) supersymmetric. We finish by performing some groundwork analysis of the resulting theory.
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