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Fermionic Modular Categories and the 16-fold Way
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 -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 with an eye towards a
classification of the low-rank cases.Comment: Latest post-referee version. Many typos fixed, many explanations
expanded, several inconsistencies corrected. 8 figure
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