A domain wall is a type of
topological soliton
A topological soliton occurs when two adjoining structures or spaces are in some way "out of phase" with each other in ways that make a seamless transition between them impossible. One of the simplest and most commonplace examples of a topological ...
that occurs whenever a discrete symmetry is spontaneously broken. Domain walls are also sometimes called kinks in analogy with closely related kink solution of the
sine-Gordon model
The sine-Gordon equation is a nonlinear hyperbolic partial differential equation in 1 + 1 dimensions involving the d'Alembert operator and the sine of the unknown function. It was originally introduced by in the course of study of sur ...
or models with polynomial potentials. Unstable domain walls can also appear if spontaneously broken discrete symmetry is approximate and there is a
false vacuum
In quantum field theory, a false vacuum is a hypothetical vacuum that is relatively stable, but not in the most stable state possible. This condition is known as metastable. It may last for a very long time in that state, but could eventually ...
.
A domain (hyper volume) is extended in three spatial dimensions and one time dimension. A domain wall is the boundary between two neighboring domains. Thus a domain wall is extended in two spatial dimensions and one time dimension.
Important examples are:
*
Domain wall (magnetism)
A domain wall is a term used in physics which can have similar meanings in magnetism, optics, or string theory. These phenomena can all be generically described as topological solitons which occur whenever a discrete symmetry is spontaneously ...
, an interface separating magnetic domains
*
Domain wall (optics), for domain walls in optics
*
Domain wall (string theory), a theoretical 2-dimensional singularity
Besides these important cases similar solitons appear in wide spectrum of the models. Here are other examples:
*Early in the universe, spontaneous breaking of discrete symmetries produced domain walls. The resulting network of domain walls influenced the late stages of cosmological inflation and the
cosmic microwave background radiation
In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all space ...
. Observations constrain the existence of stable domain walls. Models beyond the
Standard Model can account for those constraints. Unstable cosmic domain walls may decay and produce observable radiation.
*There exist a class of the
braneworld models where the brane is assumed to be a domain wall formed by interacting extra-dimensional fields.
[V. Dzhunushaliev, V. Folomeev, M. Minamitsuji, ''Thick brane solutions'', Rept.Prog.Phys. 73 (2010).] The matter is localized due to the interaction with this configuration and can leave it at sufficiently high energies. The jargon term for this domain wall is "thick brane" in contrast to the "thin brane" of the models where it is described as delta-potential or simply as some ideal surface with matter fields on it.
References
Further reading
*Vachaspati, Tanmay (2006). ''Kinks and Domain Walls: An Introduction to Classical and Quantum Solitons''. Cambridge University Press.
External links
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Solitons
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