Hedgehog compactification

We show that the presence of a hedgehog field configuration of a Higgs field, which causes spontaneous symmetry breaking of the internal symmetry, can also cause spontaneous compactification of two of the dimensions into a two-sphere. In contrast with other mechanisms of spontaneous compacification, when the higher-dimensional cosmological constant is zero, we still get a zero effective four-dimensional cosmological constant, and not a large negative curvature of four-dimensional space. In the models in which this mechanism works, the scale of symmetry breaking is fixed self-consistently to be the Planck scale.