论文标题
在所有维度上具有有限内部对称性的拓扑阶段的分类
Classification of topological phases with finite internal symmetries in all dimensions
论文作者
论文摘要
我们通过两种不同的方法在所有维度中开发了对称对称性的琐碎（SPT）顺序的数学理论和无异常的对称性富含拓扑（集合）顺序，重点是第二种方法。第一种方法是通过添加与在2D情况下进行的拓扑激发来衡量对称性，在该拓扑激发中，在该情况下，尺寸的统一融合1类别的最小模块化扩展是数学描述的。该2D结果立即概括为所有维度，除了1D以外，该维度受到特殊护理的处理。第二种方法是使用SPT/SET顺序的一维较高大量和边界捆绑关系。这种方法还导致我们在各个维度中进行了精确的数学描述和SPT/设定订单的分类。这两种方法的等效性以及已知的物理结果为我们提供了许多精确的数学预测。
We develop a mathematical theory of symmetry protected trivial (SPT) orders and anomaly-free symmetry enriched topological (SET) orders in all dimensions via two different approaches with an emphasis on the second approach. The first approach is to gauge the symmetry in the same dimension by adding topological excitations as it was done in the 2d case, in which the gauging process is mathematically described by the minimal modular extensions of unitary braided fusion 1-categories. This 2d result immediately generalizes to all dimensions except in 1d, which is treated with special care. The second approach is to use the 1-dimensional higher bulk of the SPT/SET order and the boundary-bulk relation. This approach also leads us to a precise mathematical description and a classification of SPT/SET orders in all dimensions. The equivalence of these two approaches, together with known physical results, provides us with many precise mathematical predictions.
