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    Fermionic Modular Categories and the 16-fold Way

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    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 1616-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+2PSU(2)_{4m+2} 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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