Spontaneous compactification into symmetric spaces with nonsimple holonomy group

It is shown that the compactification of the subspace of the additional dimensions into symmetric spaces with nonsimple holonomy group can be due to the interaction of the gravitational field with gauge fields that transform with respect to one of the invariant subgroups of the holonomy group, i.e., it can be realized by a smaller number of gauge fields than the compactification into symmetric spaces with simple holonomy group.