Universal Thermal Instabilities and the High-Temperature Phase of the N=4 Superstrings

Using the properties of gauged N=4 supergravity, we show that it is possible to derive a universal thermal effective potential that describes all possible high-temperature instabilities of the known N=4 superstrings. These instabilities are due to non-perturbative dyonic modes, which become tachyonic in a region of the thermal moduli space M={s,t,u}; M is common to all non-perturbative dual-equivalent N=4 superstrings in five dimensions. We analyse the non-perturbative thermal potential and show the existence of a phase transition at high temperatures corresponding to a condensation of 5-branes. This phase is described in detail, using an effective non-critical string theory.