Finite 2-group gauge theory and its 3+1D lattice realization

Abstract

In this work, we employ the Tannaka-Krein reconstruction to compute the quantum double $\mathcal{D}(\mathcal{G})$ of a finite 2-group $\mathcal{G}$ as a Hopf monoidal category. We also construct a 3+1D lattice model from the Dijkgraaf-Witten TQFT functor for the 2-group $\mathcal{G}$, generalizing Kitaev's 2+1D quantum double model. Notably, the string-like local operators in this lattice model are shown to form $\mathcal{D}(\mathcal{G})$. Specializing to $\mathcal{G}={\mathbb{Z}}_2$, we demonstrate that the topological defects in the 3+1D toric code model are modules over $\mathcal{D}({\mathbb{Z}}_2)$.

42 pages, published version. All comments are welcome

References in corpus (5)

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• Excitations in the Higher Lattice Gauge Theory Model for Topological Phases III: the (3+1)-Dimensional Case
• 2-Drinfel'd double symmetry of the 4d Kitaev model