Classification of invertible fermionic GQLs by modular extensions

Let GfG^f be a fermionic symmetry group and let \cE=sRep(Gf)\cE=\operatorname{sRep}(G^f) be the corresponding symmetric fusion category. Let \cM\cM be a modular extension of \cE\cE, and let cc denote the central charge. Fermionic GQL classification conjecture. Invertible fermionic GQLs with symmetry GfG^f are classified by (\cM,c)(\cM,c), where \cM\cM is a modular extension of \cE=sRep(Gf)\cE=\operatorname{sRep}(G^f), and cc is the central charge determining the layers of ν=8\nu=8 integer quantum Hall states. The claim is the fermionic analogue of the proposed bosonic classification; the source gives no resolution of it.

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Primary source

Tian Lan, Liang Kong and Xiao-Gang Wen, “Classification of 2+1D topological orders and SPT orders for bosonic and fermionic systems with on-site symmetries”, arXiv:1602.05946 (2017).

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