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Loops in 4+1d Topological Phases

Chen, Xie and Dua, Arpit and Hsin, Po-Shen and Jian, Chao-Ming and Shirley, Wilbur and Xu, Cenke (2021) Loops in 4+1d Topological Phases. . (Unpublished)

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2+1d topological phases are well characterized by the fusion rules and braiding/exchange statistics of fractional point excitations. In 4+1d, some topological phases contain only fractional loop excitations. What kind of loop statistics exist? We study the 4+1d gauge theory with 2-form ℤ₂ gauge field (the loop only toric code) and find that while braiding statistics between two different types of loops can be nontrivial, the self `exchange' statistics are all trivial. In particular, we show that the electric, magnetic, and dyonic loop excitations in the 4+1d toric code are not distinguished by their self-statistics. They tunnel into each other across 3+1d invertible domain walls which in turn give explicit unitary circuits that map the loop excitations into each other. The SL(2,ℤ₂) symmetry that permutes the loops, however, cannot be consistently gauged and we discuss the associated obstruction in the process. Moreover, we discuss a gapless boundary condition dubbed the 'fractional Maxwell theory' and show how it can be Higgsed into gapped boundary conditions. We also discuss the generalization of these results from the ℤ₂ gauge group to ℤ_N.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Hsin, Po-Shen0000-0002-4764-1476
Additional Information:We would like to thank Fiona Burnell, Meng Cheng, Lukasz Fidkowski, Jeongwan Haah, Yi Ni, Xiao-Liang Qi, Nathan Seiberg, Shu-Heng Shao, Kevin Walker and Zhenghan Wang for valuable discussions. A.D. thanks Yu-An Chen for the useful discussion on higher cup products. W.S., A.D., and X.C. were supported by the Simons Foundation through the collaboration on Ultra-Quantum Matter (651438, XC), the Walter Burke Institute of Theoretical Physics, the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (PHY-1733907), the National Science Foundation (DMR-1654340, XC) and the Simons Investigator Award (828078, XC). W.S. is also supported by a grant from the Simons Foundation (651444, WS). The work of P.-S. H. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632, by the Simons Foundation through the Simons Investigator Award, and by the Simons Collaboration on Global Categorical Symmetries. C. X. is supported by NSF Grant No. DMR-1920434 and the Simons Investigator program.
Group:Walter Burke Institute for Theoretical Physics, Institute for Quantum Information and Matter
Funding AgencyGrant Number
Simons Foundation651438
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Simons Foundation828078
Simons Foundation651444
Department of Energy (DOE)DE-SC0011632
Record Number:CaltechAUTHORS:20220113-234540268
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112898
Deposited By: George Porter
Deposited On:14 Jan 2022 15:53
Last Modified:02 Jun 2023 01:20

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