nLab domain wall




In general, a domain wall is a defect of codimension 1.

More specifically, in a gauge theory with a degenerate vacuum (such as when a Higgs mechanism applies), the moduli space of vacua is the quotient G/HG/H (the coset) of the gauge group GG by the stabilizer subgroup HGH \hookrightarrow G of any of these vacua (spontaneous symmetry breaking).

This means that gauge equivalence classes of vacuum configurations on a spacetime XX are given by homotopy classes of maps XΠ(G/H)X \to \Pi(G/H) (where the notation on the right denotes the underlying homotopy type of the coset space, Π\Pi is the shape modality).

If spacetime is locally to be taken of the form ×( 3D 1× 2)\mathbb{R} \times (\mathbb{R}^3 - D^1 \times \mathbb{R}^2), hence with a 1-dimensional (“wall”-like) piece taken out, them homotopy classes of maps XΠ(G/H)X \to \Pi(G/H) are classified by the 0-th homotopy group π 0(G/H)\pi_0(G/H). For a given nontrivial element here the corresponding vacuum is said to contain a domain wall defect.

For more see at QFT with defects the section Topological defects from spontaneously broken symmetry.

singularityfield theory with singularities
boundary condition/braneboundary field theory
domain wall/bi-braneQFT with defects


See also:

Last revised on January 24, 2024 at 15:38:39. See the history of this page for a list of all contributions to it.