D-Dimensional Conformal $\sigma$-models and Topological Excitations

The D-dimensional conformal nonlinear sigma-models (NSM) sre constructed. It is shown that the NSM on spaces with ${\pi }_{D-1}=\mathbb{Z}$ have the topological solutions of a “hedgehog” and “anti-hedgehog” types with logarithmic energies. For spaces with ${\pi }_D\mathrm{\ne }0$ they have also the topological excitations of instanton types with finite energies.