Non-Abelian sine-Gordon solitons: Correspondence betweenSU(N)Skyrmions andCPN−1lumps

2015/01/31 by Minoru Eto, Muneto Nitta · 36 citations
Mathematics · Physics and Astronomy · #Abelian group #Algebraic structures and combinatorial models #Ansatz #Black Holes and Theoretical Physics #Combinatorics #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Nonlinear system #Physics #Quantum mechanics #Realization (probability) #Skyrmion #Soliton #hep-ph #hep-th #sine-Gordon equation

paper · pdf · doi:10.1103/physrevd.91.085044

published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 91(8) (American Physical Society) · 24 pages, 4 figures, published version

openalex publication_date 2015/04/30 · arxiv created 2015/05/03 · arxiv updated 2015/05/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Topologically stable non-Abelian sine-Gordon solitons have been found recently in the U(N) chiral Lagrangian and a U(N) gauge theory with two N by N complex scalar fields coupled to each other. We construct the effective theory on a non-Abelian sine-Gordon soliton that is a nonlinear sigma model with the target space ℝ\ifmmode×\else\texttimes\fiℂP^N\ensuremath-1. We then show that ℂP^N\ensuremath-1 lumps on it represent SU(N) Skyrmions in the bulk point of view, providing a physical realization of the rational map ansatz for Skyrmions of the translational (Donaldson) type. We find therefore that Skyrmions can exist stably without the Skyrme term.

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