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

Abstract

We derive a partial electric-magnetic (PEM) duality transformation of the twisted quantum double (TQD) model TQD$(G,\alpha )$---discrete Dijkgraaf-Witten model---with a finite gauge group $G$, which has an Abelian normal subgroup $N$, and a three-cocycle $\alpha \in H^3(G,U(1))$. Any equivalence between two TQD models, say, TQD$(G,\alpha )$ and TQD$(G^{\prime },{\alpha }^{\prime })$, 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 $D^{\alpha }(G)$ and $D^{{\alpha }^{\prime }}(G^{\prime })$ and derive the map between the anyons of one model and those of the other.

version submitted to JHEP

References in corpus (4)

• A classification of symmetry enriched topological phases with exactly solvable models
• Twisted Quantum Double Model of Topological Phases in Two--Dimension
• Electric-magnetic duality in the quantum double models of topological orders with gapped boundaries
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