$SU(N)$ QCD（adj.）关于$\mathbb{R}^3\times S^1$
Infrared renormalon in $SU(N)$ QCD(adj.) on $\mathbb{R}^3\times S^1$
摘要：
在$n_W$味伴随Weyl费米子（QCD（adj.））的$SU(N)$规范理论中研究了胶子凝聚体中的红外重整化子。在$\mathbb{Z}_N$扭曲边界条件下对~ $\mathbb{R}^3\times S^1$进行了数值模拟。我们依赖于所谓的大- $β_0$近似作为一个传统的工具来分析重正化，其中只考虑费曼图，占主导地位的大- $n_W$极限，而真空极化的系数是由手设置的单圈β函数~ $β_0=11/3-2n_W/3$。在大-$β_0$近似下的大~ $N$极限中，获得扭曲Kaluza-Klein动量的W玻色子在~ $u=2$处产生对应于Borel奇点的重整化二义性。这提供了紧化空间~ $\mathbb{R}^3\times S^1$中的系统与非紧化空间~ $\mathbb{R}^4$中的系统具有相同的重整化模糊性的一个例子。我们还讨论了微妙的问题，博雷尔奇点的位置可以改变取决于两个必要的操作的顺序。
英文摘要：
We study the infrared renormalon in the gluon condensate in the $SU(N)$ gauge theory with $n_W$-flavor adjoint Weyl fermions (QCD(adj.)) on~$\mathbb{R}^3\times S^1$ with the $\mathbb{Z}_N$ twisted boundary conditions. We rely on the so-called large-$β_0$ approximation as a conventional tool to analyze the renormalon, in which only Feynman diagrams that dominate in the large-$n_W$ limit are considered while the coefficient of the vacuum polarization is set by hand to the one-loop beta function~$β_0=11/3-2n_W/3$. In the large~$N$ limit within the large-$β_0$ approximation, the W-boson, which acquires the twisted Kaluza--Klein momentum, produces the renormalon ambiguity corresponding to the Borel singularity at~$u=2$. This provides an example that the system in the compactified space~$\mathbb{R}^3\times S^1$ possesses the renormalon ambiguity identical to that in the uncompactified space~$\mathbb{R}^4$. We also discuss the subtle issue that the location of the Borel singularity can change depending on the order of two necessary operations.
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