标题： 规范非可逆对称性：二维量子场论中的拓扑界面和广义轨道群oid 显示英文标题

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

摘要： 在量子场论（QFT）中，对称性的规范操作是一种强大的方法，因为它可以连接不同的理论，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中离散广义对称性的规范。这种对称性由拓扑缺陷线（TDLs）描述，它们遵循通常不可逆的融合规则。尽管这一特征看似奇特，但所有已知的可逆对称性规范性质都可以推广到这种一般情况，这大大扩展了规范操作的范围和力量。这是通过用QFT之间的拓扑界面来表述广义规范操作而建立的，这解释了数学概念代数对象及其相关的模范畴在融合范畴中的代数性质，这些范畴概括了广义对称性和其规范的性质。这种观点还提供了从存在此类界面的QFT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自举的分析方法，用于分类这些拓扑界面，从而分类可能的广义规范，并在融合范畴的具体例子中演示该过程。此外，我们提出了一些例子来说明广义规范及其在具体共形场论（CFTs）中的性质。特别是，我们识别出广义轨道群oid，它捕捉了拓扑界面之间的融合结构（等价于顺序规范），以及在广义规范下CFTs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.