Generalized semilocal theories and higher Hopf maps

In semilocal theories, the vacuum manifold is fibered in a non-trivial way the action of the gauge group. Here we generalize the original semilocal theory (which was based on the Hopf bundle S ^3S1 → S ²) to realize the next Hopf bundle S ^3S3 → S ⁴, and its extensions S ^{2 n+1} → ^S3 S ⁴, and its extensions S^2n+12n+1S3 → HPⁿ. The semilocal defects in this class of theories are classified by π₃S 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 ^15S7 → S ⁸, but are able to construct other semilocal spaces realizing Stiefel bundles over grassmannian spaces.