Classification of 2+1D GQLs by bulk category, modular extension and central charge

Let \cE\cE be the symmetry category, let \cC\cC be a non-degenerate unitary braided fusion category over \cE\cE, and let \cM\cM be a modular extension of \cC\cC. Let cc be the central charge. GQL classification conjecture. 2+12+1D GQLs with symmetry \cE\cE, namely 2+12+1D SET orders, are classified by (\cC,\cM,c)(\cC,\cM,c), where \cC\cC describes the bulk topological excitations, \cM\cM describes the edge state up to E8E_8 states, and cc determines the layers of E8E_8 states. This is the paper's proposed full classification of SET and SPT orders through bulk categorical data, modular extensions and central charge; the source gives no resolution.

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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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