A Gauge Field Model On $SU(2)_L\times SU(2)_R\times U(1)_Y \times   \pi_4(G_{YM})$
  We construct a gauge field model based on $SU(2)_L\times SU(2)_R\times U(1)_Y \times \pi_4(SU(2)_L\times SU(2)_R\times U(1)_Y) $ from the principle that both the original gauge group $G_{YM}$ and the discrete group $\pi_4(G_{YM})$ should be taken as gauge groups in the sense of non-commutative geometry. We show that the Yukawa coupling and the Higgs mechanism appear as natural results. 
Bin Chen, Han-Ying Guo and Hong-Bo Teng