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

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

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  • 发表日期：

    2026年3月13日

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  • Mo Huang

摘要

In this work, we employ the Tannaka-Krein reconstruction to compute the quantum double 𝒟(𝒢) of a finite 2-group 𝒢 as a Hopf monoidal category. We also construct a 3+1D lattice model from the Dijkgraaf-Witten TQFT functor for the 2-group 𝒢, generalizing Kitaev’s 2+1D quantum double model. Notably, the string-like local operators in this lattice model are shown to form 𝒟(𝒢). Specializing to 𝒢 = ℤ2, we demonstrate that the topological defects in the 3+1D toric code model are modules over 𝒟(ℤ2).