论文标题
类$ \ mathcal {s} $理论的类的不可逆转对称性
Non-invertible Symmetries of Class $\mathcal{S}$ Theories
论文作者
论文摘要
我们研究了通过压实$ g $ g $ riemann表面上的类型$ \ mathfrak {a} _ {p-1} _ {p-1} $ 6D（2,0）理论获得的类$ \ mathcal {s} $理论的不可转化的对称性。设置了一般框架后，我们描述了如何将这种对称性分类到我们的核心5属，这是一个问题是，不可固化的对称性是否是“内在的”，即是否可以通过离散测量值与可逆的对称性有关。然后，我们描述了结果的较高维度，并解释了如何从7D Chern-Simons理论的压实中获得$ \ Mathcal {s} $类别的异常和对称性TFT以及$ n $ - 性缺陷。有趣的是，我们发现，只有通过将7D Chern-Simons理论耦合到拓扑引力，才能获得具有本质上不可矛盾的对称性理论的对称性TFT。
We study the non-invertible symmetries of class $\mathcal{S}$ theories obtained by compactifying the type $\mathfrak{a}_{p-1}$ 6d (2,0) theory on a genus $g$ Riemann surface with no punctures. After setting up the general framework, we describe how such symmetries can be classified up to genus 5. Of central interest to us is the question of whether a non-invertible symmetry is "intrinsic," i.e. whether it can be related to an invertible symmetry by discrete gauging. We then describe the higher-dimensional origin of our results, and explain how the Anomaly and Symmetry TFTs, as well as $N$-ality defects, of class $\mathcal{S}$ theories can be obtained from compactification of a 7d Chern-Simons theory. Interestingly, we find that the Symmetry TFT for theories with intrinsically non-invertible symmetries can only be obtained by coupling the 7d Chern-Simons theory to topological gravity.
