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 topological quantum field theories 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.
Publication Source (Journal or Book title)
Journal of Mathematical Physics
Bruillard, P., Galindo, C., Hagge, T., Ng, S., Plavnik, J., Rowell, E., & Wang, Z. (2017). Fermionic modular categories and the 16-fold way. Journal of Mathematical Physics, 58 (4) https://doi.org/10.1063/1.4982048