Global definition of nonlinear sigma model and some consequences

The (nonlinear) sigma model is defined as a field theory whose configurations are sections of a nontrivial fiber bundle over space-time. The action functional is a generalization of the "energy" used in the theory of harmonic maps. This definition requires minimal coupling to a Yang-Mills field, and the solutions of the coupled equations exhibit spontaneous symmetry breaking. It is shown that in a Higgs phenomenon making use of a sigma model instead of the Higgs fields, no scalars would survive symmetry breaking