A domain wall is a type of

topological soliton In mathematics and physics, solitons, topological solitons and topological defects are three closely related ideas, all of which signify structures in a physical system that are stable against perturbations. Solitons do not decay, dissipate, disper ...

that occurs whenever a

discrete symmetry In mathematics and geometry, a discrete symmetry is a symmetry that describes non-continuous changes in a system. For example, a square possesses discrete rotational symmetry, as only rotations by multiples of right angles will preserve the square ...

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 second-order nonlinear partial differential equation for a function \varphi dependent on two variables typically denoted x and t, involving the wave operator and the sine of \varphi. It was originally introduced by ...

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 state that is locally stable but does not occupy the most stable possible ground state. In this condition it is called metastable. It may last for a very long time in this stat ...

. 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) In magnetism, a domain wall is an interface separating magnetic domains. It is a transition between different magnetic moments and usually undergoes an angular displacement of 90° or 180°. A domain wall is a gradual reorientation of individu ...

, an interface separating magnetic domains *

Kink (materials science) Kinks are deviations of a dislocation defect along its glide plane. In edge dislocations, the constant glide plane allows short regions of the dislocation to turn, converting into screw dislocations and producing kinks. Screw dislocations have ro ...

, a type of

dislocation In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to sli ...

in a crystal *

Domain wall (optics) A domain wall is a term used in physics which can have similar meanings in optics, magnetism, or string theory. These phenomena can all be generically described as topological solitons which occur whenever a discrete symmetry is spontaneously b ...

, for domain walls in optics *

Domain wall (string theory) In string theory, a domain wall is a theoretical (d−1)-dimensional singularity. A domain wall is meant to represent an object of codimension one embedded into space (a defect in space localized in one spatial dimension). For example, D8-bran ...

, 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 The cosmic microwave background (CMB, CMBR), or relic radiation, is microwave radiation that fills all space in the observable universe. With a standard optical telescope, the background space between stars and galaxies is almost completely dar ...

. Observations constrain the existence of stable domain walls. Models beyond the

Standard Model The Standard Model of particle physics is the Scientific theory, theory describing three of the four known fundamental forces (electromagnetism, electromagnetic, weak interaction, weak and strong interactions – excluding gravity) in the unive ...

can account for those constraints. Unstable cosmic domain walls may decay and produce observable radiation. *There exist a class of the

braneworld Brane cosmology refers to several theories in particle physics and cosmology related to string theory, superstring theory and M-theory. Brane and bulk The central idea is that the visible, four-dimensional spacetime is restricted to a brane i ...

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.

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* Solitons {{CMP-stub

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