We construct the general vortex solution in the fully-Higgsed, color-flavor locked vacuum of a non-Abelian gauge theory, where the gauge group is taken to be the product of an arbitrary simple group and U(1), with a Fayet-Iliopoulos term. The use of holomorphic invariants extends the scope of the powerful moduli matrix formalism in which the vortex moduli spaces have been determined.
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