Electric-magnetic duality in twisted quantum double model of topological orders

A bstract We derive a partial electric-magnetic (PEM) duality transformation of the twisted quantum double (TQD) model TQD( G, α ) — discrete Dijkgraaf-Witten model — with a finite gauge group G , which has an Abelian normal subgroup N , and a three-cocycle α ∈ H 3 ( G, U(1)). Any equivalence between two TQD models, say, TQD( G, α ) and TQD( G′, α′ ), can be realized as a PEM duality transformation, which exchanges the N -charges and N -fluxes only. Via the PEM duality, we construct an explicit isomorphism between the corresponding TQD algebras D α ( G ) and D α′ ( G′ ) and derive the map between the anyons of one model and those of the other.