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valbert4 committed Nov 15, 2024
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- 'Higher gauge theory code'

description: |
A code whose codewords realize lattice two-gauge theory \cite{arXiv:math/0307200,arxiv:hep-th/0304074,arxiv:hep-th/0412325,arXiv:math/0511710,arxiv:arXiv.1002.4636,arXiv:1003.4485,arXiv:1307.4793,arxiv:1404.2634,arXiv:1308.2926} for a finite \textit{two-group} (a.k.a. a \textit{crossed module}) in arbitrary spatial dimension.
A code whose codewords realize lattice two-gauge theory \cite{arXiv:math/0307200,arxiv:hep-th/0304074,arxiv:hep-th/0412325,arXiv:math/0511710,arxiv:1002.4636,arXiv:1003.4485,arXiv:1307.4793,arxiv:1404.2634,arXiv:1308.2926} for a finite \textit{two-group} (a.k.a. a \textit{crossed module}) in arbitrary spatial dimension.
There exist several lattice-model formulations in arbitrary spatial dimension \cite{arxiv:1309.4721,arxiv:1702.00868} as well as explicitly in 3D \cite{arxiv:1606.06639,arxiv:1802.10104,arXiv:1901.02249,arXiv:1904.00994} and 4D \cite{arXiv:1904.00994}, with the 3D case realizing the Yetter model \cite{doi:10.1142/S0218216593000076,doi:10.1112/S0024610798006838,doi:10.1142/S0218216596000400,arXiv:math/9903003}.
A two-gauge theory generalizes ordinary gauge theory by replacing the gauge group with a two-group.
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