拓扑序扭曲量子双模型的电磁对偶性
Electric-Magnetic duality in twisted quantum double model of topological orders
摘要：
本文导出了扭曲量子偶（TQD）模型$(G,α)$ --离散Dijkgraaf-Witten模型--在有限规范群$G$上的部分电磁对偶变换，其中规范群$G$具有阿贝尔正规子群$N$和三上循环$α\in H^3(G,U(1))$ .两个TQD模型之间的任何等价性，比如TQD $(G,α)$和TQD $(G',α')$，都可以用一个PEM对偶变换来实现，它只交换$N$ -电荷和$N$ -通量。通过PEM对偶，我们构造了相应的TQD代数$D^α(G)$和$D^{α'}(G')$之间的显式同构，并导出了其中一个模型的任意子与另一个模型的任意子之间的映射.
英文摘要：
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 $α\in H^3(G,U(1))$. 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.
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