High Temperature Symmetry Breaking, SUSY Flat Directions, and the   Monopole Problem
  Supersymmetric flat directions allow a generic counterexample to the phenomenon of symmetry restoration at high temperatures. We show that (exponentially) large VEVs can be developed along these directions through temperature-induced `dimensional transmutation'. A minimum with broken gauge charges (e.g. electric charge) can exist at arbitrarily high temperatures. In such a scenario magnetic monopoles are never formed, independent of whether inflation occurs before or after the GUT phase transition, or whether it occurs at all. 
Gia Dvali (1) and Lawrence M. Krauss (2) ((1) New York University and   ICTP, (2) Case Western Reserve University)