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

Journal of High Energy Physics

Yuting Hu¹  Yidun Wan¹ 

[1] Department of Physics and Institute for Quantum Science and Engineering, South University of Science and Technology;

关键词: Topological States of Matter;    Anyons;    Duality in Gauge Field Theories;   

DOI  :  10.1007/JHEP11(2020)170

来源: DOAJ

【 摘 要 】

Abstract 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.

【 授权许可】

Unknown