Boundary-bulk relation in topological orders
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...
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doaj-102ded3405694b5a858a056b0d4e64022020-11-24T21:57:47ZengElsevierNuclear Physics B0550-32131873-15622017-09-01922C627610.1016/j.nuclphysb.2017.06.023Boundary-bulk relation in topological ordersLiang Kong0Xiao-Gang Wen1Hao Zheng2Department of Mathematics and Statistics, University of New Hampshire, Durham, NH 03824, USADepartment of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USADepartment of Mathematics, Peking University, Beijing, 100871, ChinaIn 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” for a given gapped boundary phase. In this paper, we show that the n+1D “bulk” phase is given by the “center” of the nD boundary phase. In other words, the geometric notion of the “bulk” 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” satisfies the same universal property as that of the “center” of an algebra in mathematics, i.e. “bulk = 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.http://www.sciencedirect.com/science/article/pii/S0550321317302183 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Liang Kong Xiao-Gang Wen Hao Zheng |
spellingShingle |
Liang Kong Xiao-Gang Wen Hao Zheng Boundary-bulk relation in topological orders Nuclear Physics B |
author_facet |
Liang Kong Xiao-Gang Wen Hao Zheng |
author_sort |
Liang Kong |
title |
Boundary-bulk relation in topological orders |
title_short |
Boundary-bulk relation in topological orders |
title_full |
Boundary-bulk relation in topological orders |
title_fullStr |
Boundary-bulk relation in topological orders |
title_full_unstemmed |
Boundary-bulk relation in topological orders |
title_sort |
boundary-bulk relation in topological orders |
publisher |
Elsevier |
series |
Nuclear Physics B |
issn |
0550-3213 1873-1562 |
publishDate |
2017-09-01 |
description |
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” for a given gapped boundary phase. In this paper, we show that the n+1D “bulk” phase is given by the “center” of the nD boundary phase. In other words, the geometric notion of the “bulk” 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” satisfies the same universal property as that of the “center” of an algebra in mathematics, i.e. “bulk = 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. |
url |
http://www.sciencedirect.com/science/article/pii/S0550321317302183 |
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