GENERALIZED SEMILOCAL THEORIES AND HIGHER HOPF MAPS

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 S3 --> S1 S2) to realize the next Hopf bundle S7 --> S3 S4, and its extensions S2n+1 - -> S3 HP(n). semilocal defects in this class of theories are classifie d by pi3(S3), and are interpreted as constrained instantons or general ized sphaleron configurations. We fail to find a field theoretic reali zation of the final Hopf bundle S15 --> S7 S8, but are able to constru ct other semilocal spaces realizing Stiefel bundles over grassmannian spaces.