QCD的红外不动点、临界味数和八元数的三重自同构
Infrared fixed point of QCD, critical flavor number and triality automorphism of octonions
摘要：
我们证明了基于t 'Hooft反常匹配条件和由薛定谔泛函方法导出的费米子$N_f^c$出现红外不动点的临界味数的差异（$N_f^c\sim 9)$和JLab组使用Bjorken求和规则和GDH求和规则的实验分析，和我们的晶格模拟（$N_f^c\sim 3$）可以通过假设红外不动点的拓扑结构不是$U(1)^3$的拓扑结构而是$G_2$的拓扑结构来解决出现在四元数乘积中的八元数。四元数实条件下的晶格模拟结果与BLM重整化理论的预测结果一致，这可能是由于四元数$S^3\times R$流形上的边界条件所致.通过沃德恒等式测量的质子的形状因子，通过在动量p+q/2和p-q/2的逆传播子的差异与唯象偶极拟合一致。
英文摘要：
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'Hooft anomaly matching condition and derived from the Schrödinger functional method ($N_f^c\sim 9)$ and the experimental analysis of the JLab group using Bjorken sum rule and GDH sum rule, and our lattice simulation($N_f^c\sim 3$) could be resolved by assuming the topological structure of the infrared fixed point is not that of $U(1)^3$ but that of $G_2$ with triality automorphism of octonions which appear in the product of quaternions. The agreement of the infrared fixed point of the running coupling measured in lattice simulations with use of the quaternion real condition and the prediction of the BLM renormalization theory might be due to the boundary condition on $S^3\times R$ manifold of quaternion. The form factor of a proton measured via Ward identity through the difference of the inverse propagator at momentum p+q/2 and at p-q/2 agrees with the phenomenological dipole fit.
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