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arXiv 1301.3209hep-th
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渐近自由矢量规范理论中$β$函数的高圈结构性质

Higher-Loop Structural Properties of the $β$ Function in Asymptotically Free Vectorial Gauge Theories

Robert Shrock

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22 pages, 4 figures
发表信息：
Phys. Rev. D 87, 105005 (2013)
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摘要：

本文研究了渐近自由矢量规范理论中$β$函数的一些高圈结构性质。我们的主要重点是理论与费米子内容，导致红外（IR）零$β$。我们提出了解析和数值计算的规范耦合的值，其中$β$达到最小值，$β$在这个最小值的值，和斜率的$β$在IR零，在两个，三个，和四个回路的顺序。$β$在IR零点处的斜率与准共形规范理论中介子质量的估计有关。导出了关于上述量与回路阶的关系的一些不等式。一个一般的不等式推导出有关的$β$的IR零点的移位，从$n$ -循环的$(n+1)$ -循环的顺序，在$β$的$(n+1)$ -循环系数的符号的依赖。对具有${\cal N}=1$超对称性的规范理论也给出了一些结果。

英文摘要：

We investigate some higher-loop structural properties of the $β$ function in asymptotically free vectorial gauge theories. Our main focus is on theories with fermion contents that lead to an infrared (IR) zero in $β$. We present analytic and numerical calculations of the value of the gauge coupling where $β$ reaches a minimum, the value of $β$ at this minimum, and the slope of $β$ at the IR zero, at two-, three-, and four-loop order. The slope of $β$ at the IR zero is relevant for estimates of a dilaton mass in quasiconformal gauge theories. Some inequalities are derived concerning the dependence of the above quantities on loop order. A general inequality is derived concerning the dependence of the shift of the IR zero of $β$, from the $n$-loop to the $(n+1)$-loop order, on the sign of the $(n+1)$-loop coefficient in $β$. Some results are also given for gauge theories with ${\cal N}=1$ supersymmetry.

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