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arXiv · 1805.10008

$SU(3)$ Knot Solitons: Hopfions in the $F_2$ Skyrme-Faddeev-Niemi model

Yuki Amari·Nobuyuki Sawado
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Abstract

We discuss the existence of knot solitons (Hopfions) in a Skryme-Faddeev-Niemi-type model on the target space $SU(3)/U(1)^2$, which can be viewed as an effective theory of both the $SU(3)$ Yang-Mills theory and the $SU(3)$ anti-ferromagnetic Heisenberg model. We derive the knot solitons with two different types of ansatz: the first is a trivial embedding configuration of $SU(2)$ into $SU(3)$, and the second is a non-embedding configuration that can be generated through the Bäcklund transformation. The resulting Euler-Lagrange equations for both ansatz reduce exactly to those of the $CP^1$ Skyrme-Faddeev-Niemi model. We also examine some quantum aspects of the solutions using the collective coordinate zero-mode quantization method.

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Yuki Amari, Nobuyuki Sawado. 2018-08-24. $SU(3)$ Knot Solitons: Hopfions in the $F_2$ Skyrme-Faddeev-Niemi model. https://doi.org/10.1016/j.physletb.2018.08.020

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