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# Topological defects

DOI link for Topological defects

Topological defects book

# Topological defects

DOI link for Topological defects

Topological defects book

## ABSTRACT

When a phase transition occurs in the early universe, the alignment of the spontaneous symmetry breaking expectation value may be different in adjacent causal domains. In that case, topologically stable objects such as domain walls, cosmic strings and magnetic monopoles, referred to as ‘topological defects’, can be formed [1]. Similar topological defects are familiar in condensed state physics. For example, a ferromagnet is, in general, divided into domains where the spontaneous magnetization is aligned in a definite direction. At the boundary between two such domains, the direction of the magnetization evolves continuously between its direction in one domain and its direction in the adjacent domain to form a so-called ‘domain wall’. Another example of a topological defect is provided by a magnetic flux line in a type II superconductor. In this case, the phase of a complex scalar field (associated with the Cooper-paired electron condensate) changes by 2πn, where n is an integer, in going around a closed loop surrounding the flux line and the flux line carries n units of a quantum of magnetic flux. In addition to these two-dimensional and one-dimensional topological defects, there are also point defects. These are most familiar in a particle physics context as magnetic monopole solutions though analogous objects occur in superfluid ^{3}He. In the context of particle physics and early cosmology, the corresponding topological defects are associated with the vacuum expectation values (VEVs) in electroweak or grand unified theories or with the various moduli that occur in superstring theories.