Fermionic modular categories and the 16-fold way Academic Article uri icon


  • 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.

published proceedings


altmetric score

  • 1

author list (cited authors)

  • Bruillard, P., Galindo, C., Hagge, T., Ng, S., Plavnik, J. Y., Rowell, E. C., & Wang, Z.

citation count

  • 51

complete list of authors

  • Bruillard, Paul||Galindo, Cesar||Hagge, Tobias||Ng, Siu-Hung||Plavnik, Julia Yael||Rowell, Eric C||Wang, Zhenghan

publication date

  • April 2017