The topic of cosmic strings provides a bridge between the physics of the very small and the very large They are predicted by some unified theories of particle interactions If they exist, they may help to explain some of the largest-scale structures seen in the Universe today They are `topological defects' that may have been formed at phase transitions in the very early history of the Universe, analogous to those found in some condensed-matter systems --- vortex lines in liquid helium, flux tubes in type-II superconductors, or disclination lines in liquid crystals In this review, we describe what they are, why they have been hypothesized and what their cosmological implications would be The relevant background from the standard models of particle physics and cosmology is described in section 1 In section 2, we review the idea of symmetry breaking in field theories, and show how the defects formed are constrained by the topology of the manifold of degenerate vacuum states We also discuss the different types of cosmic strings that can appear in different field theories Section 3 is devoted to the dynamics of cosmic strings, and section 4 to their interaction with other fields The formation and evolution of cosmic strings in the early Universe is the subject of section 5, while section 6 deals with their observational implications Finally, the present status of the theory is reviewed in section 7

Cosmic strings

We review the current status of the problem of constructing classical field theory solutions describing stationary vortex rings in Minkowski space in 3+1 dimensions. We describe the known up to date solutions of this type, such as the static knot solitons stabilized by the topological Hopf charge, the attempts to gauge them, the anomalous solitons stabilized by the Chern-Simons number, as well as the non-Abelian monopole and sphaleron rings. Passing to the rotating solutions, we first discuss the conditions insuring that they do not radiate, and then describe the spinning $Q$-balls, their twisted and gauged generalizations reported here for the first time, spinning skyrmions, and rotating monopole-antimonopole pairs. We then present the first explicit construction of global vortons as solutions of the elliptic boundary value problem, which demonstrates their non-radiating character. Finally, we describe the analogs of vortons in the Bose-Einstein condensates, analogs of spinning $Q$-balls in the non-linear optics, and also moving vortex rings in superfluid helium and in ferromagnetics.

Stationary ring solitons in field theory - knots and vortons

The effect of charge on a vortex world-sheet is examined. The relationship between world-sheet charge, winding number, and the flow of momentum along the vortex is illuminated. Full solutions for bosonic field and current profiles are obtained numerically. Both the string energy per unit length and tension are calculated. As an application stationary circular string solutions are studied. We find that except possibly for extreme cases rings stabilized by winding number alone do not exist. The role of angular momentum in stabilizing a ring is then discussed, emphasizing its model independent nature, and it is shown that in this case stationary spinning ring solutions, called vortons, are easily found. In a cosmological setting this can lead to a massive overdensity of vortons equivalent to a monopole problem. 

The physics of vortex superconductivity. II

Stationary ring solitons in field theory — Knots and vortons

Duality relation between charged elastic strings and superconducting cosmic strings

We investigate the effect that a current flowing on a superconducting string has on its motion, and demonstrate that for a wide class of models the current can build up so that the tension vanishes, leaving the string behaving more like a ''spring.'' Possible conflicts with both nucleosynthesis and constraints on gravitational radiation are briefly discussed.

Dynamics of superconducting cosmic strings

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Dynamics of superconducting cosmic strings