Topological symmetry breaking in self-interacting theories on toroidal space–time

Source abstract

The possibility of topological mass generation through symmetry breaking in a simple model consisting of a self-interacting (massive or massless) λφ4 scalar field on the space–time TN×Rn, n, N∈N0−TN being a general torus—is investigated. The nonrenormalized effective potential is calculated and the specific dependences of the generated mass on the compactification lengths and on the initial mass of the field are determined. Later, in order to obtain the renormalized topologically generated mass, the analysis is restricted 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, for n=1 and n=0 and for values of the vector of compactification lengths belonging to some specific domain of RN, symmetry breaking does actually take place. Explicit values of the mass topologically generated in this way are obtained.