Supersymmetry and finite - temperature strings ∗

We describe finite temperature N = 4 superstrings in D = 5 by an effective fourdimensional supergravity of the thermal winding modes that can become tachyonic and trigger the instabilities at the Hagedorn temperature. Using a domain-wall ansatz, exact solutions to special BPS-type first order equations are found. They preserve half of the supersymmetries, contrary to the standard perturbative superstring at finite temperature that breaks all supersymmetries. Our solutions show no indication of any tachyonic instability and provide evidence for a new BPS phase of finite temperature superstrings that is stable for all temperatures. This would have important consequences for a stringy description of the early universe. ∗Expanded version of talks given by K.S. in the 8th International Conference on Supersymmetries in Physics, CERN, Geneva, Switzerland 26 June-1 July 2000, in The Ninth Marcel Grossmann Meeting (to appear in the proccedings), Rome, July 2-8, 2000 and in the conference on Particle Physics and Gravitation: Quantum Fields and Strings, Kolymbari, Greece, 9-15 September 2000.