One-loop renormalization of a self-interacting scalar field in nonsimply connected spacetimes.

Using the effective potential, we study the one-loop renormalization of a massive self-interacting scalar field at finite temperature in flat manifolds with one or more compactified spatial dimensions. We prove that, owing to the compactification and finite temperature, the renormalized physical parameters of the theory (mass and coupling constant) acquire thermal and topological contributions. In the case of one compactified spatial dimension at finite temperature, we find that the corrections to the mass are positive, but those to the coupling constant are negative. We discuss the possibility of triviality, i.e. that the renormalized coupling constant goes to zero at some temperature or at some radius of the compactified spatial dimension. ∗Permanent address: Centro Brasileiro de Pesquisas Fisica-CBPF, Rua Dr. Xavier Sigaud 150, Rio de Janeiro, RJ 22290-180, Brazil