Topological Soliton with Nonzero Hopf Invariant in Yang-Mills-Higgs Model


We propose a topological soliton or instanton solution with nonzero Hopf invariant to the 3+1D non-Abelian gauge theory coupled with scalar fields. This solution, which we call Hopf soliton, represents a spacetime event that makes a 2π2\pi rotation of the monopole. Although the action of this Hopf soliton is logarithmically divergent, it may still give relevant contributions in a finite-sized system. Since the Chern-Simons term for the unbroken U(1)U(1) gauge field may appear in the low energy effective theory, the Hopf soliton may possibly generate fractional statistics for the monopoles.Comment: 16 pages, 1 figure

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