论文标题
6D中的较高形式对称性TFT
Higher Form Symmetries TFT in 6d
论文作者
论文摘要
$ d $维量子场理论的对称和异常通常用$（d+1）$ - 维拓扑作用编码，称为对称拓扑场理论（TFT）。我们得出了6d $（1,0）$字段理论的2形和1形对称对称的对称TFT，重点是具有单个张量多重的理论（等级1）。我们通过将低能张量分支动作与更高形式对称性的背景字段相连，并查看动力学和背景字段的对称转换规则，来实现这一点。这些转换规则还意味着在3组结构中混合了更高形式的对称性。对于某些特定且相关的较高级别案例，我们还从全息双IIA超级重力解决方案中得出了对称性TFT。对称性TFT动作包含2形对称性和1形对称背景之间的耦合，这导致通过圆形紧凑获得的5D KK理论的1形对称性之间的混合异常。我们通过由5D有效的低能库仑分支拉格朗日（Lagrangian）耦合到背景字段的纯5D分析来证实这一点。我们还针对5D $ SU（P）$ Supersymmetric Gauge理论得出对称性TFT，其Chern-Simons级别$ Q $以及在低能源时没有非亚伯利亚仪表理论描述的5D理论。最后，我们讨论了耦合到重力时的2形和1形对称性对称的命运。
Symmetries and anomalies of a $d$-dimensional quantum field theory are often encoded in a $(d+1)$-dimensional topological action, called symmetry topological field theory (TFT). We derive the symmetry TFT for the 2-form and 1-form symmetries of 6d $(1,0)$ field theories, focusing on theories with a single tensor multiplet (rank 1). We implement this by coupling the low-energy tensor branch action to the background fields for the higher-form symmetries and by looking at the symmetry transformation rules on dynamical and background fields. These transformation rules also imply a mixing of the higher-form symmetries in a 3-group structure. For some specific and related higher rank cases, we also derive the symmetry TFT from the holographic dual IIA supergravity solutions. The symmetry TFT action contains a coupling between the 2-form symmetry and the 1-form symmetry backgrounds, which leads to a mixed anomaly between the 1-form symmetries of the 5d KK-theory obtained by circle compactification. We confirm this by a pure 5d analysis provided by the 5d effective low-energy Coulomb branch Lagrangian coupled to background fields. We also derive the symmetry TFT for 5d $SU(p)$ supersymmetric gauge theories with Chern-Simons level $q$ and for 5d theories without non-abelian gauge theory description at low-energy. Finally, we discuss the fate of the 2-form and 1-form symmetry of rank 1 6d field theories when coupled to gravity.
