Symmetry non-restoration at high temperature and supersymmetry

We analyse the high temperature behaviour of softly broken supersymmetric theories taking into account the role played by effective non-renormalizable terms generated by the decoupling of superheavy degrees of freedom or the Planck scale physics. It turns out that discrete or continuous symmetries, spontaneously broken at intermediate scales, may never be restored, at least up to temperatures of the cutoff scale. There are a few interesting differences from the usual non-restoration in non-supersymmetric theories case where one needs at least two Higgs fields and non-restoration takes place for a range of parameters only. We show that with non-renormalizable interactions taken into account the non-restoration can occur for any nonzero range of parameters even for a single Higgs field. We show that such theories in general solve the cosmological domain wall problem, since the thermal production of the dangerous domain walls is enormously suppressed.