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arxiv: 1210.2233 · v3 · submitted 2012-10-08 · ✦ hep-th · cond-mat.other· hep-ph

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Correspondence between Skyrmions in 2+1 and 3+1 Dimensions

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classification ✦ hep-th cond-mat.otherhep-ph
keywords skyrmiondomainwallconstructmodelnon-abelianadmittingdimensions
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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.

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