THE UV PRICE FOR SYMMETRY NON-RESTORATION

We study the non restoration of symmetries with a local order paramete r in field theory at finite temperature. After giving an interpretatio n of the phenomenon, we show that hierarchy problems are a necessary c ondition for its realization in renormalizable theories. We then use a large N treatment, and find that high temperature symmetry can stay b roken in this limit (in opposition with a previous result), and furthe r that the running of couplings reinforces the effect in the simplest model with two scalars. (C) 1997 Published by Elsevier Science B.V.