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Dijkgraaf-Witten (DW) theories are of recent interest to the condensed mattercommunity, in part because they represent topological phases of matter, butalso because they characterize the response theory of certain symmetryprotected topological (SPT) phases. However, as yet there has not been acomprehensive treatment of the spectra of these models in the field theoreticsetting -- the goal of this work is to fill the gap in the literature, at leastfor a selection of DW models with abelian gauge groups but non-abeliantopological order. As applications, various correlation functions and fusionrules of line operators are calculated. We discuss for example the appearanceof non-abelian statistics in DW theories with abelian gauge groups.

Field Theories for Gauged Symmetry Protected Topological Phases: Abelian Gauge Theories with non-Abelian Quasiparticles