Abstract
Semilocal strings-a particular limit of electroweak strings-are an interesting example of a stable non-topological defect whose properties resemble those of their topological cousins, the Abrikosov-Nielsen-Olesen vortices. There is, however, one important difference: a network of semilocal strings will contain segments. These are 'dumbbells' whose ends behave almost like global monopoles that are strongly attracted to one another. While closed loops of string will eventually shrink and disappear, the segments can either shrink or grow, and a cosmological network of semilocal strings will reach a scaling regime. We discuss attempts to find a 'thermodynamic' description of the cosmological evolution and scaling of a network of semilocal strings, by analogy with well-known descriptions for cosmic strings and for monopoles. We propose a model for the time evolution of an overall length scale and typical velocity for the network as well as for its segments, and some supporting (preliminary) numerical evidence. This article is part of a discussion meeting issue 'Topological avatars of new physics'.
Highlights
Semilocal strings are a non-topological type of defect arising in theories with both local and global symmetries [1,2]
From a cosmological point of view, a crucial property of defect networks is that they often show scaling: after some time, statistical properties of the network such as the typical inter-defect distance become a fixed fraction of the horizon size. This is true of cosmic strings and is true of global monopoles so it is natural to ask whether a network of semilocal strings will show scaling behaviour
The velocity-dependent one-scale (VOS) model provides a quantitative and physically clear methodology to describe the evolution of topological defect networks, both in condensed matter and cosmological settings, and has been extensively compared to numerical simulations
Summary
Semilocal strings are a non-topological type of defect arising in theories with both local and global symmetries [1,2] (see [3] for a review). A more detailed argument [2] shows that the boundary between stability and instability is at β = 1, where there is a one-parameter family of neutrally stable solutions with the same energy per unit length but with varying core widths (see [1]) This is usually called the BPS or supersymmetric limit. From a cosmological point of view, a crucial property of defect networks is that they often show scaling: after some time, statistical properties of the network such as the typical inter-defect distance (or, if the defects have a spatial extension, their typical curvature radii) become a fixed fraction of the horizon size This is true of cosmic strings and is true of global monopoles so it is natural to ask whether a network of semilocal strings will show scaling behaviour. We build on these results to propose a new, improved, VOS model for semilocal networks together with some preliminary comparisons with numerical simulations
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