标题： 大尺度$N$膨胀与 SU($N$)杨-米尔斯规范场理论中的分解 显示英文标题

标题： Large $N$ scaling and factorization in SU($N$) Yang-Mills gauge theory

摘要： SU($N$) 规范理论的大型 $N$ 极限在微扰论中已有很好的理解。此外，非微扰的格点研究也提供了重要的正面证据，表明't Hooft 的预测是有效的。我们通过利用杨-米尔斯梯度流以及详细的蒙特卡洛模拟，大大超越了以往研究的统计和系统精度，针对 4 维 SU($N$) 纯规范理论进行了研究。利用 $N=3,4,5,6,8$ 的结果，我们研究了极限及其逼近过程。我们特别关注那些测试大 $N$ 极限下预期因子分解的可观测量。这些研究既在连续极限下进行，也在有限晶格间距下进行。大 $N$ 标度的非微扰验证具有很高的精度；特别是，因子分解得到了证实。 对于只探测典型约束长度尺度以下距离的量，$1/N$展开的系数为$\mathrm{O}(1)$，但我们发现大（平滑的）威尔逊圈有相当大的$\mathrm{O}(1/N^2)$校正。 当然，这种校正的确切大小还取决于当取极限时哪些量被固定住。 显示英文摘要

摘要： The large $N$ limit of SU($N$) gauge theories is well understood in perturbation theory. Also non-perturbative lattice studies have yielded important positive evidence that 't Hooft's predictions are valid. We go far beyond the statistical and systematic precision of previous studies by making use of the Yang-Mills gradient flow and detailed Monte Carlo simulations of SU($N$) pure gauge theories in 4 dimensions. With results for $N=3,4,5,6,8$ we study the limit and the approach to it. We pay particular attention to observables which test the expected factorization in the large $N$ limit. The investigations are carried out both in the continuum limit and at finite lattice spacing. Large $N$ scaling is verified non-perturbatively and with high precision; in particular, factorization is confirmed. For quantities which only probe distances below the typical confinement length scale, the coefficients of the $1/N$ expansion are of $\mathrm{O}(1)$, but we found that large (smoothed) Wilson loops have rather large $\mathrm{O}(1/N^2)$ corrections. The exact size of such corrections does, of course, also depend on what is kept fixed when the limit is taken.