Classification of topological phases with finite internal symmetries in all dimensions
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Author(s)
Kong, Liang
Lan, Tian
Wen, Xiao-Gang
Zhang, Zhi-Hao
Zheng, Hao
Date Issued
September 2020
Journal
Journal of High Energy Physics
Publisher
Springer Berlin Heidelberg
Citation
Kong, Liang et al., "Classification of topological phases with finite internal symmetries in all dimensions." Journal of High Energy Physics 2020, 9 (September 2020): 93 doi. 10.1007/JHEP09(2020)093 ©2020 Authors
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Final published version
Abstract
We develop a mathematical theory of symmetry protected trivial (SPT) orders and anomaly-free symmetry enriched topological (SET) orders in all dimensions via two different approaches with an emphasis on the second approach. The first approach is to gauge the symmetry in the same dimension by adding topological excitations as it was done in the 2d case, in which the gauging process is mathematically described by the minimal modular extensions of unitary braided fusion 1-categories. This 2d result immediately generalizes to all dimensions except in 1d, which is treated with special care. The second approach is to use the 1-dimensional higher bulk of the SPT/SET order and the boundary-bulk relation. This approach also leads us to a precise mathematical description and a classification of SPT/SET orders in all dimensions. The equivalence of these two approaches, together with known physical results, provides us with many precise mathematical predictions. ©2020
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1007/JHEP09(2020)093
