We derive a universal thermal effective potential, which describes all poss
ible high-temperature instabilities of the known N = 4 superstrings, using
the properties of gauged N = 4 supergravity, These instabilities are due to
three non-perturbative thermal dyonic modes, which become tachyonic in a r
egion of the thermal moduli space. The latter is described by three moduli,
s, t, u, which are common to all non-perturbative dual-equivalent strings
with N = 4 supersymmetry in five dimensions: the heterotic on T-4 X S-1, th
e type IIA on K-3 X S-1, the type IIB on K-3 X S-1 and the type I on T-4 X
S-1. The non-perturbative instabilities are analyzed. These strings undergo
a high-temperature transition to a new phase in which five-branes condense
. This phase is described in detail, using both the effective supergravity
and non-critical string theory in six dimensions. In the new phase, supersy
mmetry is perturbatively restored but broken at the non-perturbative level.
In the infinite-temperature limit the theory is topological with an N = 2
supersymmetry based on a topologically non-trivial hyper-Kahler manifold. (
C) 1999 Elsevier Science B.V. All rights reserved.