Proceedings of the

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.

Fri Jun 20 15:40:05 BST 1997