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arXiv:2512.19608

Higher lattice gauge theory from representations of 2-groups and 3+1D topological phases

Latévi M. Lawson, Prince K. Osei

hep-latcond-mat.otherhep-thmath-phquant-phSubmitted Dec 22, 2025• Announced Dec 23, 2025• 0 citations
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Abstract

We construct a higher lattice gauge theory based on the representation of 2-groups described by a category of crossed modules on a lattice model described by path 2-groupoids. Using these lattice gauge representations, an exactly solvable Hamiltonian for topological phases in 3+1 dimensions is constructed. We show that the ground states of this model are topological observables.

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48 pages

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