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Topological Quantum Field Theory for Abelian Topological Phases and Loop Braiding Statistics in (3+1)-Dimensions

Qing-Rui Wang Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong Meng Cheng Department of Physics, Yale University, New Haven, Connecticut 06511-8499, USA Chenjie Wang Department of Physics, City University of Hong Kong, Kowloon, Hong Kong; Department of Physics and Center of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China Zheng-Cheng Gu Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong

Mathematical Physics arXiv subject: High Energy Physics - Theory (hep-th) arXiv subject: Strongly Correlated Electrons (cond-mat.str-el) mathscidoc:2206.22004

PHYSICAL REVIEW B, 99, 235137, 2019.6
Topological qauntum field theory(TQFT) is a very powerful theoretical tool to study topological phases and phase transitions. In 2+1D, it is well known that the Chern-Simons theory captures all the universal topological data of topological phases, e.g., quasi-particle braiding statistics, chiral central charge and even provides us a deep insight for the nature of topological phase transitions. Recently, topological phases of quantum matter are also intensively studied in 3+1D and it has been shown that loop like excitation obeys the so-called three-loop-braiding statistics. In this paper, we will try to establish a TQFT framework to understand the quantum statistics of particle and loop like excitation in 3+1D. We will focus on Abelian topological phases for simplicity, however, the general framework developed here is not limited to Abelian topological phases.
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@inproceedings{qing-rui2019topological,
  title={Topological Quantum Field Theory for Abelian Topological Phases and Loop Braiding Statistics in (3+1)-Dimensions},
  author={Qing-Rui Wang, Meng Cheng, Chenjie Wang, and Zheng-Cheng Gu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220616163425078265391},
  booktitle={PHYSICAL REVIEW B},
  volume={99},
  pages={235137},
  year={2019},
}
Qing-Rui Wang, Meng Cheng, Chenjie Wang, and Zheng-Cheng Gu. Topological Quantum Field Theory for Abelian Topological Phases and Loop Braiding Statistics in (3+1)-Dimensions. 2019. Vol. 99. In PHYSICAL REVIEW B. pp.235137. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220616163425078265391.
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