D-Dimensional Conformal $σ$-models and Topological Excitations

Abstract

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