In semilocal theories, the vacuum manifold is fibered in a non- trivial way by the action of the gauge group. Here we generalize the original semilocal theory (which was based on the Hopf bundle S(sup 3) (yields)(sup S1) S(sup 2)) to realize the next Hopf bundle S(sup 7) (yields)(sup S3) S(sup 1), and its extensions S(sup 2n+1 yields)(sup S3) HP(sup n). The semilocal defects in this class of theories are classified by (pi)(sub 3)(S (sup 3)), and are interpreted as constrained instantons or generalized sphaleron configurations. We fail to find a field theoretic realization of the final Hopf bundle S(sup 15) (yields)(sup S7) S(sup 8), but are able to construct other semilocal spaces realizing Stiefel bundles over Grassmanian spaces.
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