Fig. 6: Wilson loop calculation of a three-dimensional gauge field.

a–c Theoretical calculation and d–f numerical simulation results of the Wilson loop ∣WCW∣ versus parameters of the applied gauge field θ1, θ2, ϕ1, and ϕ2 for θ2 = 0, π/2, and π, respectively. Here, ∣WCW∣ ≠3 is a necessary but insufficient condition for a non-Abelian gauge field.