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 f2 × G. The quaternion group makes a surprise appearance.
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ArXiv ePrint: 1605.01640
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Bhardwaj, L., Gaiotto, D. & Kapustin, A. State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter. J. High Energ. Phys. 2017, 96 (2017). https://doi.org/10.1007/JHEP04(2017)096
- Anomalies in Field and String Theories
- Discrete Symmetries
- Topological Field Theories
- Topological States of Matter