Braiding statistics and link invariants of bosonic/fermionic topological quantum matter in 2+ 1 and 3+ 1 dimensions

Pavel Putrov Juven Wang Shing-Tung Yau

Theoretical Physics mathscidoc:1912.43540

Annals of Physics, 384, 254-287, 2017.9
Abstract Topological Quantum Field Theories (TQFTs) pertinent to some emergent low energy phenomena of condensed matter lattice models in 2+ 1 and 3+ 1 dimensions are explored. Many of our TQFTs are highly-interacting without free quadratic analogs. Some of our bosonic TQFTs can be regarded as the continuum field theory formulation of DijkgraafWitten twisted discrete gauge theories. Other bosonic TQFTs beyond the DijkgraafWitten description and all fermionic TQFTs (namely the spin TQFTs) are either higher-form gauge theories where particles must have strings attached, or fermionic discrete gauge theories obtained by gauging the fermionic Symmetry-Protected Topological states (SPTs). We analytically calculate both the Abelian and non-Abelian braiding statistics data of anyonic particle and string excitations in these theories, where the statistics data can one-to-one characterize the underlying
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@inproceedings{pavel2017braiding,
  title={Braiding statistics and link invariants of bosonic/fermionic topological quantum matter in 2+ 1 and 3+ 1 dimensions},
  author={Pavel Putrov, Juven Wang, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203921061500104},
  booktitle={Annals of Physics},
  volume={384},
  pages={254-287},
  year={2017},
}
Pavel Putrov, Juven Wang, and Shing-Tung Yau. Braiding statistics and link invariants of bosonic/fermionic topological quantum matter in 2+ 1 and 3+ 1 dimensions. 2017. Vol. 384. In Annals of Physics. pp.254-287. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203921061500104.
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