BPS Sphalerons in the $F_2$ Non-Linear Sigma Model

Abstract

We construct static and also time-dependent solutions in a non-linear sigma model with target space being the flag manifold $F_2=SU(3)/U(1{)}^2$ on the four dimensional Minkowski space-time by analytically solving the second order Euler-Lagrange equation. We show the static solutions saturate an energy lower bound and can be derived from coupled first order equations though they are saddle point solutions. We also discuss basic properties of the time-dependent solutions.

10 pages, 5 figures

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Cited by in corpus (6)

• Flag manifold sigma models: spin chains and integrable theories
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• $\mathbb{C}{P}^2$ Skyrmion Crystals in an SU(3) Magnet with a Generalized Dzyaloshinskii-Moriya Interaction
• Fractional Skyrmion molecules in a $\mathbb{C}{P}^{N-1}$ model
• $SU(3)$ Knot Solitons: Hopfions in the $F_2$ Skyrme-Faddeev-Niemi model
• Oscillator Calculus on Coadjoint Orbits and Index Theorems