State sum constructions of spinTFTs and string net constructions of fermionic phases of matter
It is possible to describe fermionic phases of matter and spintopological field theories in 2+1d in terms of bosonic “shadow” theories, which are obtained from the original theory by “gauging fermionic parity”. Furthemore, the fermionic/spin theories are recovered from their shadow by a process of fermionic anyon condensation: gauging a oneform symmetry generated by quasiparticles with fermionic statistics. We apply the formalism to theories which admit gapped boundary conditions. We obtain TuraevVirolike and LevinWenlike constructions of fermionic phases of matter. Here, we describe the group structure of fermionic SPT phases protected by Z _{2}f × G. The quaternion group makes a surprise appearance.
 Authors:

^{[1]};
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^{[2]}
 Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
 California Inst. of Technology (CalTech), Pasadena, CA (United States). Dept. of Physics
 Publication Date:
 Grant/Contract Number:
 SC0011632
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 4; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Research Org:
 California Inst. of Technology (CalTech), Pasadena, CA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), High Energy Physics (HEP) (SC25)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Anomalies in Field and String Theories; Discrete Symmetries; Topological Field Theories; Topological States of Matter
 OSTI Identifier:
 1393477
Bhardwaj, Lakshya, Gaiotto, Davide, and Kapustin, Anton. State sum constructions of spinTFTs and string net constructions of fermionic phases of matter. United States: N. p.,
Web. doi:10.1007/JHEP04(2017)096.
Bhardwaj, Lakshya, Gaiotto, Davide, & Kapustin, Anton. State sum constructions of spinTFTs and string net constructions of fermionic phases of matter. United States. doi:10.1007/JHEP04(2017)096.
Bhardwaj, Lakshya, Gaiotto, Davide, and Kapustin, Anton. 2017.
"State sum constructions of spinTFTs and string net constructions of fermionic phases of matter". United States.
doi:10.1007/JHEP04(2017)096. https://www.osti.gov/servlets/purl/1393477.
@article{osti_1393477,
title = {State sum constructions of spinTFTs and string net constructions of fermionic phases of matter},
author = {Bhardwaj, Lakshya and Gaiotto, Davide and Kapustin, Anton},
abstractNote = {It is possible to describe fermionic phases of matter and spintopological field theories in 2+1d in terms of bosonic “shadow” theories, which are obtained from the original theory by “gauging fermionic parity”. Furthemore, the fermionic/spin theories are recovered from their shadow by a process of fermionic anyon condensation: gauging a oneform symmetry generated by quasiparticles with fermionic statistics. We apply the formalism to theories which admit gapped boundary conditions. We obtain TuraevVirolike and LevinWenlike constructions of fermionic phases of matter. Here, we describe the group structure of fermionic SPT phases protected by Z2f × G. The quaternion group makes a surprise appearance.},
doi = {10.1007/JHEP04(2017)096},
journal = {Journal of High Energy Physics (Online)},
number = 4,
volume = 2017,
place = {United States},
year = {2017},
month = {4}
}