Symmetry Non-restoration at High Temperature

We discuss the (non)-restoration of global and local symmetries at high temperature. First, we analyze a two-scalar model with $Z_2\times Z_2$ symmetry using the exact renormalization group. We conclude that inverse symmetry breaking is possible in this kind of models within the perturbative regime. Regarding local symmetries, we consider the $SU(2)\otimes U(1)$ gauge symmetry and focus on the case of a strongly interacting scalar sector. Employing a model-independent chiral Lagrangian we find indications of symmetry restoration.