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

Yuting Hu, Yidun Wan

Published 2020-07-30Version 1

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 $G$ and a three-cocycle $\alpha \in H^3(G,U(1))$ . Such a gauge group $G$ is required to bear an Abelian normal subgroup $N$. The PEM duality transformation exchanges the $N$-charges and $N$-fluxes only. The PEM duality exists only under certain conditions, by which a TQD model is better reformulated as a bilayer model. Any equivalence between two TQD models, say, TQD$(G,\alpha)$ and TQD$(G',\alpha')$, can be realized as a PEM duality transformation.