  We study BPS non-abelian semilocal vortices in U(Nc) gauge theory with Nf
flavors, Nf > Nc, in the Higgs phase. The moduli space for arbitrary winding
number is described using the moduli matrix formalism. We find a relation
between the moduli spaces of the semilocal vortices in a Seiberg-like dual
pairs of theories, U(Nc) and U(Nf-Nc). They are two alternative regularizations
of a "parent" non-Hausdorff space, which tend to the same moduli space of
sigma-model lumps in the infinite gauge coupling limits. We examine the
normalizability of the zero-modes and find the somewhat surprising phenomenon
that the number of normalizable zero-modes, dynamical fields in the effective
action, depends on the point of the moduli space we are considering. We find,
in the lump limit, an effective action on the vortex worldsheet, which we
compare to that found by Shifman and Yung.
