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

A bstract 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 2 , we demonstrate that the topological defects in the 3+1D toric code model are modules over 𝒟(ℤ 2 ).