Topological excitations of D-dimensional conformal nonlinear σ-models

Conformal nonlinear sigma -models (NSM) are constructed in arbitrary D-dimensional spaces. For odd D they are always nonlocal. It is shown that the conformal NSM on spaces with pi (D-1)=Z have topological solutions of "hedgehog" and "anti-hedgehog" types with logarithmic energies. For spaces with pi (D) not equal 0 they have also topological excitations of instanton type with finite energies. The possible interesting manifolds are discussed.