论文标题
关于拓扑订单的分类
On the classification of topological orders
论文作者
论文摘要
我们将扩展的运算符以拓扑秩序（可能是重力异常，可能具有退化地面状态），以单型karoubi纯$ n $ n $分类为单位，这些类别是有可能可划合的并且具有琐碎的中心。二元定义性编码“拓扑”一词，我们将其视为“（可分离）多输入$ n $ -scategory”的定义；中心的琐碎性实现了“远程可检测性”的物理原理。我们表明，这种$ n $ - 类别的代数是可变的（在适当的更高Morita类别中），从而识别具有异常延伸的TQFTS的拓扑订单。我们使用无中心编织的融合$（n { - } 1）$ - 类别确定无中心融合$ n $ -n $类别（即具有不可兼容单元的多键$ n $ - 类别）。然后，我们在低时空维度中讨论分类，特别是证明了所有$（1 {+} 1）$ - 和$（3 {+} 1）$ - 尺寸拓扑订单，具有任意对称性增强的，都是适当的培养基拓扑Sigma模型。这些数学结果证实并扩展了X.G.的一系列猜想和建议。 Wen等。
We axiomatize the extended operators in topological orders (possibly gravitationally anomalous, possibly with degenerate ground states) in terms of monoidal Karoubi-complete $n$-categories which are mildly dualizable and have trivial centre. Dualizability encodes the word "topological," and we take it as the definition of "(separable) multifusion $n$-category"; triviality of the centre implements the physical principle of "remote detectability." We show that such $n$-categorical algebras are Morita-invertible (in the appropriate higher Morita category), thereby identifying topological orders with anomalous fully-extended TQFTs. We identify centreless fusion $n$-categories (i.e. multifusion $n$-categories with indecomposable unit) with centreless braided fusion $(n{-}1)$-categories. We then discuss the classification in low spacetime dimension, proving in particular that all $(1{+}1)$- and $(3{+}1)$-dimensional topological orders, with arbitrary symmetry enhancement, are suitably-generalized topological sigma models. These mathematical results confirm and extend a series of conjectures and proposals by X.G. Wen et al.
