Global definition of nonlinear sigma model and some consequences

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Abstract
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.

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