Generalized Semilocal Theories and Higher Hopf Maps

Details Generalized Semilocal Theories and Higher Hopf Maps Generalized Semilocal Theories and Higher Hopf Maps

1992-09-23

arxiv.org/abs/hep-th/9209088v1

Nucl.Phys. B404 (1993) 794-804

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, uses amssymbols.sty

Scientific paper

10.1016/0550-3213(93)90597-I

\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 $\mon$) to realize the next Hopf bundle $\inst$, and its extensions $S^{2n+1}\stackrel{S^3}\rightarrow \H P^n$. 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 $\octo$, but are able to construct other semilocal spaces realizing Stiefel bundles over Grassmanian spaces.

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