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arXiv · 1603.09294

Fermionic Modular Categories and the 16-fold Way

Paul Bruillard·Cesar Galindo·Tobias Hagge·Siu-Hung Ng·Julia Yael Plavnik·Eric C. Rowell·Zhenghan Wang
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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.

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Paul Bruillard, Cesar Galindo, Tobias Hagge, Siu-Hung Ng, Julia Yael Plavnik, Eric C. Rowell, Zhenghan Wang. 2016-03-30. Fermionic Modular Categories and the 16-fold Way. https://doi.org/10.1063/1.4982048

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