State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter
Abstract
It is possible to describe fermionic phases of matter and spin-topological field theories in 2+1d in terms of bosonic "shadow" theories, which are obtained from the original theory by "gauging fermionic parity". The fermionic/spin theories are recovered from their shadow by a process of fermionic anyon condensation: gauging a one-form symmetry generated by quasi-particles with fermionic statistics. We apply the formalism to theories which admit gapped boundary conditions. We obtain Turaev-Viro-like and Levin-Wen-like constructions of fermionic phases of matter. We describe the group structure of fermionic SPT phases protected by ℤ_2^f × G. The quaternion group makes a surprise appearance.
Additional Information
© The Author(s) 2017. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Received: September 28, 2016. Accepted: February 3, 2017. Published: April 18, 2017. Article funded by SCOAP3. We thank V. Ostrik for explaining the results of [36] to one of us (A.K.). We are grateful to J. Brundan and A. Ellis for making their results [26] available prior to publication. We also thank A. Karagiozova for helping LB and DG code the figures. A. K. is grateful to J. Morgan for communicating to him the unpublished results of J. Morgan and G. Brumfiel which helped to detect an error in the first version of the paper. The research of LB and DG was supported by the Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development and Innovation. The work of A. K. was supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632 Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.Attached Files
Published - art_3A10.1007_2FJHEP04_282017_29096.pdf
Submitted - 1605.01640.pdf
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Additional details
- Eprint ID
- 76932
- Resolver ID
- CaltechAUTHORS:20170426-065601568
- Perimeter Institute for Theoretical Physics
- Industry Canada
- Ontario Ministry of Economic Development and Innovation
- DE-SC0011632
- Department of Energy (DOE)
- SCOAP3
- Created
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2017-04-26Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field