Correspondence between Skyrmions in 2+1 and 3+1 Dimensions
arXiv:1210.2233 · doi:10.1103/PhysRevD.87.025013
Abstract
A lump (2D Skyrmion) can be constructed as a sine-Gordon kink (1D Skyrmion) inside a domain wall in the massive O(3) sigma model. In this paper, we discuss relations between Skyrmions in 2+1 and 3+1 dimensions. We first construct a Bogomol'nyi-Prasad-Sommerfield 3D Skyrmion as a lump inside a non-Abelian domain wall in an O(4) sigma model with a potential term admitting two discrete vacua. Next, we construct a conventional 3D Skyrmion as a baby Skyrmion in a non-Abelian domain wall in the Skyrme model with a modified mass term admitting two discrete vacua. We also construct a spinning 3D Skyrmion as a Q-lump in the non-Abelian domain wall.
18 pages, 3 figures, v2: typos corrected, minor changes, references added, v3: published version
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