On Gauging Symmetry of Modular Categories
On Gauging Symmetry of Modular Categories
复制标题
论模范畴的对称性
DOI：
10.1007/s00220-016-2633-8
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发表时间：
2015
影响因子：
2.4
通讯作者：
Zhenghan Wang
中科院分区：
文献类型：
--
作者：
Shawn X. Cui;César Galindo;J. Plavnik;Zhenghan Wang
两个空间维度中物质拓扑相的拓扑顺序由酉模（张量）类别（UMC）编码。拓扑相的群对称性会导致其相应 UMC 的群对称性。测量是一种众所周知的理论工具，可将全局对称性提升为局部规范对称性。我们根据更高类别形式主义给出了衡量的数学公式。粗略地说，给定具有对称群 G 的 UMC，测量过程分为两步：首先将 UMC 扩展到 G 交叉编织融合类别，然后对所得类别进行等变化。测量可以判断物质的两个丰富的拓扑相是否不同，并且还提供了一种从旧的 UMC 中构建新的 UMC 的方法。我们推导了$${H^4}$$H4障碍物的公式，证明了测量的一些性质，并针对两个具体例子进行了测量。
Topological order of a topological phase of matter in two spacial dimensions is encoded by a unitary modular (tensor) category (UMC). A group symmetry of the topological phase induces a group symmetry of its corresponding UMC. Gauging is a well-known theoretical tool to promote a global symmetry to a local gauge symmetry. We give a mathematical formulation of gauging in terms of higher category formalism. Roughly, given a UMC with a symmetry group G, gauging is a 2-step process: first extend the UMC to a G-crossed braided fusion category and then take the equivariantization of the resulting category. Gauging can tell whether or not two enriched topological phases of matter are different, and also provides a way to construct new UMCs out of old ones. We derive a formula for the $${H^4}$$H4-obstruction, prove some properties of gauging, and carry out gauging for two concrete examples.