A classification of 3+1D bosonic topological orders (I): the case when point-like excitations are all bosons

Abstract

Topological orders are new phases of matter beyond Landau symmetry breaking. They correspond to patterns of long-range entanglement. In recent years, it was shown that in 1+1D bosonic systems there is no nontrivial topological order, while in 2+1D bosonic systems the topological orders are classified by a pair: a modular tensor category and a chiral central charge. In this paper, we propose a partial classification of topological orders for 3+1D bosonic systems: If all the point-like excitations are bosons, then such topological orders are classified by unitary pointed fusion 2-categories, which are one-to-one labeled by a finite group $G$ and its group 4-cocycle ${\omega }_4\in {\mathcal{H}}^4[G;U(1)]$ up to group automorphisms. Furthermore, all such 3+1D topological orders can be realized by Dijkgraaf-Witten gauge theories.

An important new result "Untwisted sector of dimension reduction is the Drinfeld center of E" is added in Sec. IIIC; other minor refinements and improvements; 23 pages, 10 figures

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