标题： 非可逆对称性作为有限群规范理论中的凝聚缺陷 显示英文标题

标题： Non-Invertible Symmetries as Condensation Defects in Finite-Group Gauge Theories

摘要： 在近期的工作中，我们发展了一种方法，用于构造有限群规范理论中的可逆和不可逆对称性，作为格点上的拓扑域壁。 在目前的工作中，我们考虑一般时空维度下的阿贝尔和非阿贝尔有限群规范理论，并展示如何将这些对称性实现为凝聚缺陷，即作为合适插入的低维拓扑算符。 然后，我们利用这些对称性的凝聚表达式及其构成低维对象的代数性质来计算它们的融合规则和作用。 我们在$\mathbb{Z}_N$规范理论中阐明了这一讨论，其中我们推导了由子群标记的域壁与加倍规范群的作用之间的对应关系，以及由全局对称性的子代数标记的高阶规范凝聚缺陷之间的对应关系。 作为一个主要应用，我们得到了由规范群外自同构定义的阿贝尔规范理论的可逆对称性的凝聚表达式。 我们还展示了如何使用这些思想来推导某些非阿贝尔群的作用。 例如，可以通过规范交换对称性来获得二面体群$\mathbb{D}_4$在$\mathbb{Z}_2\times\mathbb{Z}_2$规范理论中的作用。 显示英文摘要

摘要： In recent work, we developed a method to construct invertible and non-invertible symmetries of finite-group gauge theories as topological domain walls on the lattice. In the present work, we consider abelian and non-abelian finite-group gauge theories in general spacetime dimension, and demonstrate how to realize these symmetries as condensation defects, i.e., as suitable insertions of lower dimensional topological operators. We then compute the fusion rules and action of these symmetries using their condensation expression and the algebraic properties of the lower dimensional objects that make them. We illustrate the discussion in $\mathbb{Z}_N$ gauge theory, where we derive the correspondence between domain walls, labeled by subgroups and actions for the doubled gauge group, and higher gauging condensation defects, labeled by subalgebras of the global symmetry. As a primary application, we obtain the condensation expression for the invertible symmetries of abelian gauge theories defined by outer automorphisms of the gauge group. We also show how to use these ideas to derive the action for certain non-abelian groups. For instance, one can obtain the action for the Dihedral group $\mathbb{D}_4$ by gauging a swap symmetry of $\mathbb{Z}_2\times\mathbb{Z}_2$ gauge theory.