论文标题
通用的不可逆转对称性
Universal Non-Invertible Symmetries
论文作者
论文摘要
众所周知，在量子场理论中测量有限的0形式对称性会导致由拓扑Wilson线缺陷产生的双重对称性。这些由形成1类别的0形对称组的表示形式描述。我们认为，对于d维量子场理论，一组双对称性的组合实际上要大得多，并且由（D-1） - 类别描述，该类别是由低维拓扑量子场理论形成的，具有相同的0形式对称性。我们详细研究了由2D拓扑量子场理论以0形式对称性描述的（D-1） - 类别的两类（D-1）类别。我们进一步表明，这两个类别的对象是最近讨论的2D缩合缺陷，该缺陷是由威尔逊线的高级命名所构建的。同样，通过测量任何更高形式或更高组对称性获得的双对称性也形成了A（D-1） - 类别是由低维拓扑量子场理论形成的，具有更高或更高的对称性。一个特别有趣的案例是与有限2组对称性相关的两类对称性的两类，因为它描述了通过测量（d-3） - 形式对称性作用的0形式对称性引起的不可变形对称性。最近在文献中通过其他方法研究了这种不可变形的对称性，我们的结果不仅与以前的结果一致，而且我们的方法还提供了一种更简单的方法来计算这些不可逆转的对称性的各种属性。我们描述了如何将结果应用于各种时空维度的各种规格理论的不可变形对称性。我们还讨论了由任何任意量子场理论中2D缩合缺陷形成的2类。
It is well-known that gauging a finite 0-form symmetry in a quantum field theory leads to a dual symmetry generated by topological Wilson line defects. These are described by the representations of the 0-form symmetry group which form a 1-category. We argue that for a d-dimensional quantum field theory the full set of dual symmetries one obtains is in fact much larger and is described by a (d-1)-category, which is formed out of lower-dimensional topological quantum field theories with the same 0-form symmetry. We study in detail a 2-categorical piece of this (d-1)-category described by 2d topological quantum field theories with 0-form symmetry. We further show that the objects of this 2-category are the recently discussed 2d condensation defects constructed from higher-gauging of Wilson lines. Similarly, dual symmetries obtained by gauging any higher-form or higher-group symmetry also form a (d-1)-category formed out of lower-dimensional topological quantum field theories with that higher-form or higher-group symmetry. A particularly interesting case is that of the 2-category of dual symmetries associated to gauging of finite 2-group symmetries, as it describes non-invertible symmetries arising from gauging 0-form symmetries that act on (d-3)-form symmetries. Such non-invertible symmetries were studied recently in the literature via other methods, and our results not only agree with previous results, but our approach also provides a much simpler way of computing various properties of these non-invertible symmetries. We describe how our results can be applied to compute non-invertible symmetries of various classes of gauge theories with continuous disconnected gauge groups in various spacetime dimensions. We also discuss the 2-category formed by 2d condensation defects in any arbitrary quantum field theory.
