High Temperature Symmetry Nonrestoration

Naively one expects that at low temperature a system has less symmetry than at high temperature. However, there are cases in nature, where the opposite happens. This phenomenon is called inverse symmetry breaking. A very similar phenomenon is symmetry nonrestoration at high temperature. It appears when the system has at high T less symmetry than allowed by the Lagrangian, which means that some vev is nonzero. With high temperature we mean temperature higher than any parameter of mass dimension in the Lagrangian. In this short review we will describe some examples of this phenomenon both in nature and in field theory. Due to lack of space many topics will be mentioned only briefly. The interested reader can refer to some other reviews 1 as well as to the original papers.