Symmetry breaking and defects

TL;DR

This paper reviews symmetry-breaking phase transitions, the formation of topological defects, their classification, and experimental tests in condensed matter systems that mimic early Universe phenomena.

Contribution

It provides a comprehensive overview of symmetry breaking, defect formation, and experimental analogs, integrating condensed matter and cosmological perspectives.

Findings

Topological defects are stable and influence system behavior.

Classification of defects via homotopy groups.

Laboratory experiments simulate early Universe defect formation.

Abstract

Symmetry-breaking phase transitions are ubiquitous in condensed matter systems and in quantum field theories. There is also good reason to believe that they feature in the very early history of the Universe. At many such transitions topological defects of one kind or another are formed. Because of their inherent stability, they can have important effects on the subsequent behaviour of the system. In the first of these lectures I shall review a number of examples of spontaneous symmetry breaking, many of which will be discussed in more detail by other lecturers, and discuss their general features. The second lecture will be mainly devoted to the conditions under which topological defects can appear and their classification in terms of homotopy groups of the underlying vacuum manifold. In my final lecture, I will discuss the `cosmology in the laboratory' experiments which have been done to try to test some of the ideas thrown up by discussions of defect formation in the early Universe by looking at analogous processes in condensed-matter systems.