标题： 非可逆对称性的规范：二维量子场论中的拓扑界面和广义 orbifold 群oid 显示英文标题

标题： Gauging Non-Invertible Symmetries: Topological Interfaces and Generalized Orbifold Groupoid in 2d QFT

摘要： 对称性规范（gauging）是量子场论（QFT）中对称性的一种强有力的运算，因为它能够连接不同的理论，并揭示给定理论中的隐藏结构。 我们开始系统地研究二维QFT中的离散广义对称性的规范。 这些对称性由拓扑缺陷线（TDLs）描述，它们遵循一般情况下非可逆的融合规则。 尽管具有这种看似奇特的特征，所有关于规范可逆对称性的已知性质都适用于这一更一般的设定，这大大扩展了规范的作用范围和能力。 这是通过用QFT之间的拓扑界面来表述广义规范实现的，这解释了代数对象及其在融合范畴上的模范畴的数学概念背后的物理图像，这些概念封装了广义对称性和其规范的代数性质。 这种观点还提供了从QFT的基本公理性质出发，对范畴论中已知数学定理的简单物理推导。 我们讨论了一种类似于“bootstrap”分析的方法来分类这样的拓扑界面，从而确定可能的广义规范，同时在具体的融合范畴例子中演示了这一过程。 此外，我们给出了多个例子来说明具体共形场论（CFT）中的广义规范及其特性。 特别是，我们识别出了广义规范下的自同构群系（generalized orbifold groupoid），它捕捉了拓扑界面（等价于顺序规范）之间的融合结构以及CFT中大量新的自对偶性。 显示英文摘要

摘要： Gauging is a powerful operation on symmetries in quantum field theory (QFT), as it connects distinct theories and also reveals hidden structures in a given theory. We initiate a systematic investigation of gauging discrete generalized symmetries in two-dimensional QFT. Such symmetries are described by topological defect lines (TDLs) which obey fusion rules that are non-invertible in general. Despite this seemingly exotic feature, all well-known properties in gauging invertible symmetries carry over to this general setting, which greatly enhances both the scope and the power of gauging. This is established by formulating generalized gauging in terms of topological interfaces between QFTs, which explains the physical picture for the mathematical concept of algebra objects and associated module categories over fusion categories that encapsulate the algebraic properties of generalized symmetries and their gaugings. This perspective also provides simple physical derivations of well-known mathematical theorems in category theory from basic axiomatic properties of QFT in the presence of such interfaces. We discuss a bootstrap-type analysis to classify such topological interfaces and thus the possible generalized gaugings and demonstrate the procedure in concrete examples of fusion categories. Moreover we present a number of examples to illustrate generalized gauging and its properties in concrete conformal field theories (CFTs). In particular, we identify the generalized orbifold groupoid that captures the structure of fusion between topological interfaces (equivalently sequential gaugings) as well as a plethora of new self-dualities in CFTs under generalized gaugings.