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arXiv · 2007.15636

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

Yuting Hu·Yidun Wan
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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$(G',\alpha')$, 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 $D^{\alpha'}(G')$ and derive the map between the anyons of one model and those of the other.

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Yuting Hu, Yidun Wan. 2020-07-30. Electric-Magnetic duality in twisted quantum double model of topological orders. https://doi.org/10.1007/jhep11(2020)170

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