Boundary-bulk relation in topological orders
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j.nuclphysb.2017.06.023_pdfa.pdf
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Author(s)
Kong, Liang
Zheng, Hao
Wen, Xiao-Gang
Date Issued
July 2017
Journal
Nuclear Physics B
Publisher
Elsevier
Citation
Kong, Liang, et al. “Boundary-Bulk Relation in Topological Orders.” Nuclear Physics B 922 (September 2017): 62–76 © 2017 The Author(s)
Version
Final published version
Abstract
In this paper, we study the relation between an anomaly-free n+1 D topological order, which are often called n+1 D topological order in physics literature, and its n D gapped boundary phases. We argue that the n+1 D bulk anomaly-free topological order for a given n D 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+1 D “ bulk ” phase is given by the “center” of the n D 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.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1016/j.nuclphysb.2017.06.023
