What does this research mean for the field?

The quantum double of a finite 2-group can be realized as a Hopf monoidal category in a 3+1D lattice model, with string-like local operators forming this quantum double. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

This research aims to explore the quantum double of finite 2-groups using Tannaka-Krein reconstruction and to build a corresponding 3+1D lattice model.

March 16, 2026Open Access

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

Key Points

This research aims to explore the quantum double of finite 2-groups using Tannaka-Krein reconstruction and to build a corresponding 3+1D lattice model.
Employed Tannaka-Krein reconstruction for calculating quantum doubles.
Constructed a 3+1D lattice model utilizing Dijkgraaf-Witten TQFT functor.
Specialized the model to the case of the finite group ℤ2.
The constructed model's local operators form the quantum double D(ℤ2).
Demonstrated that topological defects in the 3+1D toric code model behave as modules over D(ℤ2).

Abstract

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 ).

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

Key Points

Abstract

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