  It is shown that conformally invariant theories can be obtained within the
framework of the coset space construction. The corresponding technique is
applicable for the construction of representations of the unbroken conformal
group, as well as of a spontaneously broken one. A special role of the
"Nambu-Goldstone fields" for special conformal transformations is clarified -
they ensure self-consistency of a theory by guaranteeing that discrete
symmetries are indeed symmetries of the theory. A generalization of the
developed construction to a special class of symmetry groups with a non-linear
realization of its discrete elements is given. Based on these results, the
usage of the inverse Higgs constraints for the conformal group undergoing
spontaneous symmetry breaking is questioned.
