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We show that the discrepancy on the critical flavor number of fermions$N_f^c$ for the appearance of the infrared fixed point based on the t'Hooftanomaly matching condition and derived from the Schr\"odinger functional method($N_f^c\sim 9)$ and the experimental analysis of the JLab group using Bjorkensum rule and GDH sum rule, and our lattice simulation($N_f^c\sim 3$) could beresolved by assuming the topological structure of the infrared fixed point isnot that of $U(1)^3$ but that of $G_2$ with triality automorphism of octonionswhich appear in the product of quaternions.  The agreement of the infrared fixed point of the running coupling measured inlattice simulations with use of the quaternion real condition and theprediction of the BLM renormalization theory might be due to the boundarycondition on $S^3\times R$ manifold of quaternion. The form factor of a protonmeasured via Ward identity through the difference of the inverse propagator atmomentum p+q/2 and at p-q/2 agrees with the phenomenological dipole fit.

Infrared fixed point of QCD, critical flavor number and triality automorphism of octonions