HEDGEHOG COMPACTIFICATION

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