Symmetry Restoration and Breaking at Finite Temperature: An Introductory Review

Symmetries at finite temperature are of great importance to understand dynamics of spontaneous symmetry breaking phenomena, especially phase transitions in early Universe. Some symmetries such as the electroweak symmetry can be restored in hot environment. However, it is a nontrivial question that the phase transition occurs via first or second order, or even smooth crossover, which strongly depends on underlying physics. If it is first order, gravitational waves can be generated, providing a detectable signal of this epoch. Moreover, the baryon asymmetry of the Universe can also arise under some conditions. In this article, the electroweak phase transition is reviewed, focusing particularly on the case of the first-order phase transition. Much attention is paid to multi-step phase transitions in which additional symmetry breaking such as a spontaneous $Z_2$ breaking plays a pivotal role in broadening the possibility of the first-order electroweak phase transition. On the technical side, we review thermal resummation that mitigates a bad infrared behavior related to the symmetry restoration. In addition, gauge and scheme dependences of perturbative calculations are also briefly discussed. View Full-Text