TOPOLOGICAL SYMMETRY-BREAKING IN SELF-INTERACTING THEORIES ON TOROIDAL SPACE-TIME

The possibility of topological mass generation through symmetry breaki ng in a simple model consisting of a self-interacting (massive or mass less) lambdaphi4 scalar field on the space-time T(N) X R(n), n, N is-a n-element-of N0 - T(N) being a general torus-is investigated. The nonr enormalized effective potential is calculated and the specific depende nces of the generated mass on the compactification lengths and on the initial mass of the field are determined. Later, in order to obtain th e renormalized topologically generated mass, the analysis is restricte d to n + N = 4 dimensions. It is shown that if the field is massive no symmetry breaking can occur. On the contrary, when it is massless, fo r n = 1 and n = 0 and for values of the vector of compactification len gths belonging to some specific domain of R(N), symmetry breaking does actually take place. Explicit values of the mass topologically genera ted in this way are obtained.