On supersymmetry at high temperature

While it is possible to find examples of field theories with a spontaneously broken symmetry at high temperature, in renormalizable supersymmetric models any internal symmetry gets always restored. Recently, a counterexample was suggested in the context of nonrenormalizable supersymmetric theories. We show that non-negligible higher loop effects actually restore the symmetry, without compromising the validity of perturbation theory. We give some arguments as to why the proposed mechanism should not work in general.