Fermionic Modular Categories and the 16-fold Way
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ID: 282306
2016
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Abstract
We study spin and super-modular categories systematically as inspired by
fermionic topological phases of matter, which are always fermion parity
enriched and modelled by spin TQFTs at low energy. We formulate a $16$-fold way
conjecture for the minimal modular extensions of super-modular categories to
spin modular categories, which is a categorical formulation of gauging the
fermion parity. We investigate general properties of super-modular categories
such as fermions in twisted Drinfeld doubles, Verlinde formulas for naive
quotients, and explicit extensions of $PSU(2)_{4m+2}$ with an eye towards a
classification of the low-rank cases.
| Reference Key |
wang2016fermionic
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|---|---|
| Authors | Paul Bruillard; Cesar Galindo; Tobias Hagge; Siu-Hung Ng; Julia Yael Plavnik; Eric C. Rowell; Zhenghan Wang |
| Journal | arXiv |
| Year | 2016 |
| DOI |
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