Cobordisms and semiclassical instability of torodial compactifications

We show that toroidal compactifications of the multidimensional Minkowski space-time are semiclassically unstable due to topology change of the initial data hypersurface. Instanton solutions corresponding to tunnelling between different topologies are presented. These solutions have two pseudo-riemannian sections which can be interpreted either as the multidimensional “black holes” of Myers and Perry or as a “bubble Universe”. The second interpretation seems to be the most natural as it leads to the picture of the decay of the “false” vacuum by nucleation of bubbles of the true vacuum. The cobordism theory approach to topology change and “superselection rules” are presented. We discuss the possible semiclassical instabilities of the Calabi-Yau compactifications. It is argued, contrary to a recent statement in literature, that, as long as N = 1 four-dimensional SUSY is not spontaneously broken semiclassically, the number of generations of fundamental fermions in the low energy limit is conserved.