The UV price for symmetry non-restoration

Abstract : We study the non restoration of symmetries with a local order parameter in field theory at finite temperature. After giving an interpretation of the phenomenon, we show that hierarchy problems are a necessary condition for its realization in renormalizable theories. We then use a large N treatment, and find that high temperature symmetry can stay broken in this limit (in opposition with a previous result), and further that the running of couplings reinforces the effect in the simplest model with two scalars. @ 1997 Published by Elsevier Science B.V.