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.