SUPERSTRING PHASE-TRANSITION AT HIGH-TEMPERATURE

We analyse the phase transition of superstring at high temperature. We derive the exact effective potential of the "T-winding" mode which becomes tachyonic above the Hagedorn temperature. We show that in the heterotic case a phase transition occurs which, from the world-sheet point of view, is a generalization of the Kosterlitz-Thouless transition. We derive the conformal field theory describing the new phase and we find that the central charge of the system c is lowered by two units. The resulting high-temperature phase then corresponds to a non-critical superstring in (7 + 1 ) dimensions. Moreover, the new vacuum exhibits a miraculous "space-like" supersymmetry which leads to the vanishing of the free energy, at least up to the one-loop level. We finally argue that our result could describe a transition from a "cold" to a "hot" phase in the history of the early universe.