Topological defects (Vilenkin & Shellard (1985), Vilenkin (1985), Preskill (1984)) are stable field configurations (solitons: Rajaraman (1987)) that arise in field theories with spontaneously broken discrete or continuous symmetries. Depending on the topology of the vacuum manifold they are usually identified as domain walls (Vilenkin (1985), Preskill (1984)) (kink solutions: Rajaraman (1987)) when , as strings (Nielsen & Olesen (1973)) and one-dimensional textures (ribbons: Bachas & Tomaras (1994), Bachas & Tomaras (1995)) when , as monopoles (gauged: t'Hooft (1974), Polyakov (1974), Dokos & Tomaras (1980), or global: Barriola & Vilenkin (1989), Perivolaropoulos (1992)) and two dimensional textures ( solitons Belavin & Polyakov (1975), Rajaraman (1987)) when and three dimensional textures (Turok (1989)), skyrmions: Skyrme (1961)) when . They are expected to be remnants of phase transitions (Kibble (1976), Kolb & Turner (1990)) that may have occurred in the early universe. They also form in various condensed matter systems which undergo low temperature transitions (Zurek (1985), Zurek (1996)). Topological defects appear to fall in two broad categories. In the first one the topological charge becomes non-trivial due to the behaviour of the field configuration at spatial infinity. The symmetry of the vacuum gets restored at the core of the defect. Domain walls, strings and monopoles belong to this class of symmetric defects.
In the second category the vacuum manifold gets covered completely as the field varies over the whole of coordinate space. Moreover its value at infinity is identified with a single point of the vacuum manifold. Textures (Turok (1989)) (skyrmions: Skyrme (1961)), solitons (Belavin & Polyakov (1975)) (two dimensional textures: Turok (1989)) and ribbons (Bachas & Tomaras (1994)) belong to this class which we will call for definiteness texture-like defects. The objective of the present discussion is to present examples of defects which belong to neither of the two categories, namely the field variable covers the whole vacuum manifold at infinity with the core remaining in the non-symmetric phase. For definiteness we will call these non-symmetric defects.
Examples of non-symmetric defects have been discussed previously in the literature. Vilenkin & Everett (1982) in particular, pointed out the existence of domain walls and strings with non-symmetric cores which are unstable though to shrinking and collapse due to their string tension. A particular case of non-symmetric gauge defect was recently considered by Benson & Bucher (1993), who pointed out that the decay of an electroweak semi-local string leads to a gauged ``skyrmion'' with non-symmetric core and topological charge at infinity. This skyrmion however, rapidly expands and decays to the vacuum.
In the present talk we review recent work where we presented more examples of topological defects that belong to what we defined as the ``non-symmetric'' class. We will study in detail the properties of global domain walls in section and of global vortices in section . In both cases we will identify the parameter ranges for stability of the configurations with either a symmetric or a non-symmetric core. For the case of a domain wall wall we will discuss results of a simulation for an expanding bubble of a domain wall.
Finally, in section 4 we conclude, summarise and discuss the outlook of this work.