Classification of ( 3 + 1 ) D Bosonic Topological Orders: The Case When Pointlike Excitations Are All Bosons

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 in1+1Dbosonic systems, there is no nontrivial topological order, while in2+1Dbosonic systems, the topological orders are classified by the following pair: a modular tensor category and a chiral central charge. In this paper, following a new line of thinking, we find that in3+1Dthe classification is much simpler than it was thought to be; we propose a partial classification of topological orders for3+1Dbosonic systems: If all the pointlike excitations are bosons, then such topological orders are classified by a simpler pair(G,ω4): a finite groupGand its group 4-cocycleω4∈H4[G;U(1)](up to group automorphisms). Furthermore, all such3+1Dtopological orders can be realized by Dijkgraaf-Witten gauge theories.