论文标题
$ \ mathbb {r}^3 \ times s^1 $：I。abelian对称和中间量表的有效字段理论中的拓扑术语和异常匹配
Topological terms and anomaly matching in effective field theories on $\mathbb{R}^3\times S^1$: I. Abelian symmetries and intermediate scales
论文作者
论文摘要
我们明确地计算出$ \ mathbb {r}^3 \ times s^1 $的IR有效字段理论中出现的拓扑术语。然后，我们展示这些术语如何匹配紫外线描述的所有全局对称性't Hooft异常。我们将讨论限制在Abelian 0形式对称性的理论上，即具有一种伴随的Weyl fermion和一种或零的Dirac Fermions风味的理论。尽管根据需要保持异常匹配，但它采用与以前想象的不同形式。例如，立方和混合$ u（1）$异常与局部背景依赖性拓扑术语（背景tqfts）而不是手性 - 拉格朗日wess-zumino术语相匹配。我们还以一种新颖的方式描述了超黄米尔斯理论的磁性双重对话背景的耦合，并在整个RG流中有效，并且与单调的nopole-instanton t Hooffertices一致。我们使用它来讨论磁双重混合中心异常的匹配。
We explicitly calculate the topological terms that arise in IR effective field theories for $SU(N)$ gauge theories on $\mathbb{R}^3 \times S^1$ by integrating out all but the lightest modes. We then show how these terms match all global-symmetry 't Hooft anomalies of the UV description. We limit our discussion to theories with abelian 0-form symmetries, namely those with one flavour of adjoint Weyl fermion and one or zero flavours of Dirac fermions. While anomaly matching holds as required, it takes a different form than previously thought. For example, cubic- and mixed-$U(1)$ anomalies are matched by local background-field-dependent topological terms (background TQFTs) instead of chiral-lagrangian Wess-Zumino terms. We also describe the coupling of 0-form and 1-form symmetry backgrounds in the magnetic dual of super-Yang-Mills theory in a novel way, valid throughout the RG flow and consistent with the monopole-instanton 't Hooft vertices. We use it to discuss the matching of the mixed chiral-center anomaly in the magnetic dual.
