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

TL;DR

This paper constructs D-dimensional conformal nonlinear sigma-models and demonstrates the existence of topological solutions, including hedgehog, anti-hedgehog, and instanton types, with specific energy properties based on the space's topology.

Contribution

It introduces a new class of conformal sigma-models in arbitrary dimensions and characterizes their topological excitations and energy behaviors.

Findings

Existence of hedgehog and anti-hedgehog solutions with logarithmic energies.

Presence of instanton solutions with finite energies in certain topological spaces.

Topological solutions depend on the homotopy groups of the underlying space.

Abstract

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 $\pi_D \ne 0$ they have also the topological excitations of instanton types with finite energies.