论文标题
$ n = 2 $大吗？
Is $N=2$ Large?
论文作者
论文摘要
我们通过晶格数值模拟研究了4D SU（2）纯Yang-Mills理论的真空能量的$θ$依赖性。详细研究了拓扑激发对涂片程序的响应，以便从涂抹量规配置中提取拓扑信息。我们确定真空能量的$θ$扩展中的前两个系数，拓扑敏感性$χ$和第一个无量纲系数$ b_2 $，在连续限制下。我们发现SU（2）结果的一致性与大型$ n $缩放。通过将$ n $的颜色数量（$ n $）延续到非全能值，我们推断出SU（N）量规理论真空结构的相图作为$ n $和$θ$的函数。基于数值结果，我们提供了定量证据，表明$θ=π$的4D SU（2）Yang-Mills理论与CP对称性的自发断裂相处。
We study $θ$ dependence of the vacuum energy for the 4d SU(2) pure Yang-Mills theory by lattice numerical simulations. The response of topological excitations to the smearing procedure is investigated in detail, in order to extract topological information from smeared gauge configurations. We determine the first two coefficients in the $θ$ expansion of the vacuum energy, the topological susceptibility $χ$ and the first dimensionless coefficient $b_2$, in the continuum limit. We find consistency of the SU(2) results with the large $N$ scaling. By analytic continuing the number of colors, $N$, to non-integer values, we infer the phase diagram of the vacuum structure of SU(N) gauge theory as a function of $N$ and $θ$. Based on the numerical results, we provide quantitative evidence that 4d SU(2) Yang-Mills theory at $θ= π$ is gapped with spontaneous breaking of the CP symmetry.
