Wormholes and the construction of compactified phases

In the context of Classical General Relativity, assuming the positive energy condition, we study the possibility of connecting a region where some dimensions are compact to another region where compactification does not exist. In some simple models, where compactification is achieved through the condensation of gauge fields, we find that the matching of these two regions implies the existence of a wormhole. We also discuss the possibility of spontaneous quantum nucleation of a compactified phase in the midst of an uncompactified space.