Incarnations of instantons

Yang–Mills instantons in a pure Yang–Mills theory in four Euclidean space can be promoted to particle-like topological solitons in d=4+1d=4+1 dimensional space–time. When coupled to Higgs fields, they transform themselves in the Higgs phase into Skyrmions, lumps and sine-Gordon kinks, when trapped inside a non-Abelian domain wall, non-Abelian vortex and monopole string, respectively. Here, we point out that a closed monopole string, non-Abelian vortex sheet and non-Abelian domain wall in S1S1, S2S2 and S3S3 shapes, respectively, are all Yang–Mills instantons if their S1S1, S2S2 and S3S3 moduli, respectively, are twisted along their world-volumes.