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In physics, a domain wall is any of several similar things in string theory, magnetism, or optics. These phenomena can all be generically described as topological solitons that occur whenever a discrete symmetry is spontaneously broken.
String theory
In string theory, a domain wall is a theoretical 2-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-branes are domain walls in type II string theory. In M-theory, the existence of Horava–Witten domain walls, "ends of the world" that carry an E8 gauge theory, is important for various relations between superstring theory and M-theory.
If domain walls exist, it seems plausible that gravitational waves would be violently emitted if two such walls collided. As gravitational waves have been discovered by LIGO, it means that fundamentally, singularities plausibly exist, what type of singularities will depend on the math and observations involved.