Fermionic modular categories and the 16-fold way

被引：64

作者：

Bruillard, Paul ^{[1
]}

Galindo, Cesar ^{[2
]}

Hagge, Tobias ^{[1
]}

Ng, Siu-Hung ^{[3
]}

Plavnik, Julia Yael ^{[4
]}

Rowell, Eric C. ^{[4
]}

Wang, Zhenghan ^{[5
,6
]}

机构：

[1] Pacific Northwest Natl Lab, 902 Battelle Blvd, Richland, WA 99354 USA

[2] Univ Los Andes, Dept Matemat, Bogota, Colombia

[3] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA

[4] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

[5] Univ Calif Santa Barbara, Microsoft Res Stn Q, Santa Barbara, CA 93106 USA

[6] Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2017年 / 58卷 / 04期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1063/1.4982048

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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 by AIP Publishing.

引用

页数：31

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