论文标题
Yang-Mills理论和QCD中的中心涡流和与异常的压缩
Center vortex and confinement in Yang-Mills theory and QCD with anomaly-preserving compactifications
论文作者
论文摘要
我们构建了4D量规理论的反应压缩，包括$ SU（N）$ Yang-Mills理论，$ \ Mathcal {n} = 1 $ supersymmetric yang-mills Theory和QCD，通过通过$ t^2 $打开't Hooft Flux，以降至2D。它提供了一个新的框架来分析计算非扰动性能，例如限制，手性对称性破坏和真空的多支分支结构。我们根据中心涡流对这些现象进行了半经典描述，并表明它具有与原始$ 4 $ D量规理论相同的异常匹配条件。我们猜想，小$ t^2 \ times \ mathbb {r}^2 $上的弱耦合真空结构是绝热连接到$ \ mathbb {r}^4 $上的强耦合方案，而没有任何相位过渡。在带有基本夸克的QCD中，我们可以通过激活$ su（n_f）_ {\ mathrm {v}} $对称性转折来打开Hooft Flux，或者通过引入Baryon Number $ U（1）_ {\ Mathrm Mathriare $ n_f = n $ n_f = n $ for $ n_f = n $ for $ n_f = n $。在这两种情况下，弱耦合中心 - 涡流理论都提供了与手性拉格朗日人$ 4 $ d QCD一致的预测。
We construct an anomaly-preserving compactification of 4d gauge theories, including $SU(N)$ Yang-Mills theory, $\mathcal{N}=1$ supersymmetric Yang-Mills theory, and QCD, down to 2d by turning on 't Hooft flux through $T^2$. It provides a new framework to analytically calculate nonperturbative properties such as confinement, chiral symmetry breaking, and multi-branch structure of vacua. We give the semiclassical description of these phenomena based on the center vortex and show that it enjoys the same anomaly matching condition with the original $4$d gauge theory. We conjecture that the weak-coupling vacuum structure on small $T^2 \times \mathbb{R}^2$ is adiabatically connected to the strong-coupling regime on $\mathbb{R}^4$ without any phase transitions. In QCD with fundamental quarks as well, we can turn on 't Hooft flux either by activating $SU(N_f)_{\mathrm{V}}$ symmetry twist for $N_f=N$ flavors or by introducing a magnetic flux of baryon number $U(1)_{\mathrm{B}}$ for arbitrary $N_f$ flavors. In both cases, the weak-coupling center-vortex theory gives the prediction consistent with chiral Lagrangian of $4$d QCD.
