On the stability of toroidally compact Kaluza-Klein theories

We study the stability ar the one loop level, of finite temperature Kaluza-Klein theories coupled to matter fields. We restrict our attention to space-times containing compact manifolds which are toruses and Klein bottles. If the cosmological constant is chosen so that the effective potential vanishes at its minimum, and if twisted bosons or untwisted fermions are introduced into the theory, then these space-times are stable below a critical temperature of the order of the particle masses. We also discuss some subtleties that arises when Fermi fields are defined on non-simply connected manifolds.