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

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.