论文标题
Omega vs. Pi和6D异常取消
Omega vs. pi, and 6d anomaly cancellation
论文作者
论文摘要
在本说明中，我们回顾了同质组在确定非扰动（此后“全局”）规范异常方面的作用，鉴于最近使用Bordism了解全球异常的进展。我们解释了为什么不对$π_d（g）$的不变既不是必要的也不是足够的条件，因为在$ d $维的手性仪表理论中可能存在全球异常，并带有规格组$ g $。为了展示足够的失败，我们重新访问了以前在6D仪表理论中研究的“全球异常”。即使$π_6（g）\ neq 0 $，Bordism组$ω_7^\ mathrm {spin}（bg）$在所有三种情况下都消失了，这意味着没有全局异常。在$ g = su（2）$的情况下，我们仔细审查同型的作用，并解释为什么从Bordism的角度来看，任何7维映射的圆环都必须微不足道。在所有这些6D示例中，以前认为取消全球异常所必需的条件实际上是局部异常消失的必要条件。
In this note we review the role of homotopy groups in determining non-perturbative (henceforth `global') gauge anomalies, in light of recent progress understanding global anomalies using bordism. We explain why non-vanishing of $π_d(G)$ is neither a necessary nor a sufficient condition for there being a possible global anomaly in a $d$-dimensional chiral gauge theory with gauge group $G$. To showcase the failure of sufficiency, we revisit `global anomalies' that have been previously studied in 6d gauge theories with $G=SU(2)$, $SU(3)$, or $G_2$. Even though $π_6(G) \neq 0$, the bordism groups $Ω_7^\mathrm{Spin}(BG)$ vanish in all three cases, implying there are no global anomalies. In the case of $G=SU(2)$ we carefully scrutinize the role of homotopy, and explain why any 7-dimensional mapping torus must be trivial from the bordism perspective. In all these 6d examples, the conditions previously thought to be necessary for global anomaly cancellation are in fact necessary conditions for the local anomalies to vanish.
