Fermionic Modular Categories and the 16-fold Way

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 $16$-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.

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

References in corpus (6)

• Non-Abelian Anyons and Topological Quantum Computation
• Modular extensions of unitary braided fusion categories and 2+1D topological/SPT orders with symmetries
• Classification of abelian spin Chern-Simons theories
• Group-theoretical properties of nilpotent modular categories
• On the Gauge Equivalence of Twisted Quantum Doubles of Elementary Abelian and Extra-Special 2-Groups
• From Quantum Groups to Unitary Modular Tensor Categories

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