English

Fermionic Modular Categories and the 16-fold Way

Quantum Algebra 2017-05-24 v3

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 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.

Keywords

Cite

@article{arxiv.1603.09294,
  title  = {Fermionic Modular Categories and the 16-fold Way},
  author = {Paul Bruillard and Cesar Galindo and Tobias Hagge and Siu-Hung Ng and Julia Yael Plavnik and Eric C. Rowell and Zhenghan Wang},
  journal= {arXiv preprint arXiv:1603.09294},
  year   = {2017}
}

Comments

Latest post-referee version. Many typos fixed, many explanations expanded, several inconsistencies corrected. 8 figures

R2 v1 2026-06-22T13:21:41.701Z