SU(3) knot solitons: Hopfions in the F2 Skyrme–Faddeev–Niemi model

Abstract

We discuss the existence of knot solitons (Hopfions) in a Skyrme–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 CP1 Skyrme–Faddeev–Niemi model. We also examine some quantum aspects of the solutions using the collective coordinate zero-mode quantization method.