Topological solitons in Kaluza-Klein theories

The space of internal metrics of a Kaluza-Klein theory can inherit a complicated topology from the group of diffeomorphisms of the internal manifold. It is shown that this structure frequently gives rise to topological solitons, field configurations which cannot evolve into the vacuum in the distant future. A simple model with internal space $S^2$×$S^1$ is investigated in detail. It is found that the solitons in this model, like those in the Skyrme model, can be quantized as fermions. Kaluza-Klein theories may thus admit half-integral spin without elementary spinors.