Formation of topological defects in gauge field theories

When a symmetry gets spontaneously broken in a phase transition, topological defects are typically formed. The theoretical picture of how this happens in a breakdown of a global symmetry, the Kibble-Zurek mechanism, is well established and has been tested in various condensed matter experiments. However, from the viewpoint of particle physics and cosmology, gauge Field theories are more relevant than global theories. In recent years, there have been significant advances in the theory of defect formation in gauge field theories, which make precise predictions possible, and in experimental techniques that can be used to test these predictions in superconductor experiments. This opens up the possibility of carrying out relatively simple and controlled experiments, in which the nonequilibrium phase transition dynamics of gauge field theories can be studied. This will have a significant impact on our understanding of phase transitions in the early universe and in heavy ion collider experiments. In this paper, I review the current status of the theory and the experiments in which it can be tested.