Boundary-bulk relation in topological orders
Boundary-bulk relation in topological orders
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DOI：
10.1016/j.nuclphysb.2017.06.023
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发表时间：
2017-09-01
影响因子：
2.8
通讯作者：
Zheng, Hao
中科院分区：
文献类型：
--
作者：
Kong, Liang;Wen, Xiao-Gang;Zheng, Hao
本文研究了无反常的n+1D拓扑序(在物理文献中常称为n+1D拓扑序)与它的ND间隙边界相之间的关系。我们认为，对于给定的带隙边界相，n+1维体无反常拓扑序是唯一的。这种唯一性定义了给定有间隙的边界相的“(主体)杆下”的概念。在本文中，我们证明了棒“相下的n+1D”(体相)是由ND边界相的“中心”给出的。换句话说，“杆下(体积)”的几何概念精确地对应于“中心”的代数概念。为此，我们首先引入了同维两个(潜在反常)拓扑序之间的态射的概念，然后证明了“杆下的(体量)”的概念满足与数学中代数的“中心”相同的普适性质，即“(体量)下的杆=中心”。整个论证不需要我们知道一个(潜在反常的)拓扑序的精确数学描述。这一结果导致了具体的物理预测。(三)2017年提交人(S)。爱思唯尔出版公司(Elsevier B.V.)
In this paper, we study the relation between an anomaly-free n+1D topological order, which are often called n+1D topological order in physics literature, and its nD gapped boundary phases. We argue that the n+1D bulk anomaly-free topological order for a given nD gapped boundary phase is unique. This uniqueness defines the notion of the "(bulk) under bar" for a given gapped boundary phase. In this paper, we show that the n+1D "(bulk) under bar" phase is given by the "center" of the nD boundary phase. In other words, the geometric notion of the "(bulk) under bar" corresponds precisely to the algebraic notion of the " center". We achieve this by first introducing the notion of a morphism between two (potentially anomalous) topological orders of the same dimension, then proving that the notion of the "(bulk) under bar" satisfies the same universal property as that of the " center" of an algebra in mathematics, i.e. "(bulk) under bar= center". The entire argument does not require us to know the precise mathematical description of a (potentially anomalous) topological order. This result leads to concrete physical predictions. (C) 2017 The Author(s). Published by Elsevier B.V.