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 2f × G. The quaternion group makes a surprise appearance.

Details

Title
State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter
Author
Bhardwaj Lakshya 1 ; Gaiotto Davide 1 ; Kapustin Anton 2 

 Perimeter Institute for Theoretical Physics, Waterloo, Canada (GRID:grid.420198.6) (ISNI:0000 0000 8658 0851) 
 California Institute of Technology, Department of Physics, Pasadena, U.S.A. (GRID:grid.20861.3d) (ISNI:0000000107068890) 
Publication year
2017
Publication date
Apr 2017
Publisher
Springer Nature B.V.
e-ISSN
10298479
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
1891155855
Copyright
© The Author(s) 2017. This work is published under https://creativecommons.org/licenses/by/4.0 (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.