Generalized Semilocal Theories and Higher Hopf Maps

Abstract

\def\mon{S^3\stackrel{S^1}{\rightarrow}S^2} \def\inst{S^7\stackrel{S^3}{\rightarrow}S^4} \def\octo{S^{15}\stackrel{S^7}{\rightarrow}S^8} 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 $\text{mon}$) to realize the next Hopf bundle $\text{inst}$, and its extensions $S^{2n+1}\stackrel{S^3}{\to }{\stackrel{˝}{P}}^n$. The semilocal defects in this class of theories are classified by ${\pi }_3(S^3)$, and are interpreted as constrained instantons or generalized sphaleron configurations. We fail to find a field theoretic realization of the final Hopf bundle $\text{octo}$, but are able to construct other semilocal spaces realizing Stiefel bundles over Grassmanian spaces.

Comments: 15 pages, uses amssymbols.sty