{
"id": "2007.15636",
"version": "v1",
"published": "2020-07-30T17:55:33.000Z",
"updated": "2020-07-30T17:55:33.000Z",
"title": "Electric-Magnetic duality in twisted quantum double model of topological orders",
"authors": [
"Yuting Hu",
"Yidun Wan"
],
"categories": [
"cond-mat.str-el",
"hep-th",
"math-ph",
"math.MP"
],
"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 $G$ 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.",
"revisions": [
{
"version": "v1",
"updated": "2020-07-30T17:55:33.000Z"
}
],
"analyses": {
"keywords": [
"twisted quantum double model",
"electric-magnetic duality",
"topological orders",
"pem duality transformation exchanges",
"tqd model"
],
"note": {
"typesetting": "TeX",
"pages": 0,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}