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 -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.
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