Finite 2-group gauge theory and its 3+1D lattice realization
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908884816363520 |
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| author | Huang, Mo |
| author_facet | Huang, Mo |
| contents | In this work, we employ the Tannaka-Krein reconstruction to compute the quantum double $\mathcal D(\mathcal G)$ of a finite 2-group $\mathcal G$ as a Hopf monoidal category. We also construct a 3+1D lattice model from the Dijkgraaf-Witten TQFT functor for the 2-group $\mathcal G$, generalizing Kitaev's 2+1D quantum double model. Notably, the string-like local operators in this lattice model are shown to form $\mathcal D(\mathcal G)$. Specializing to $\mathcal G = \mathbb{Z}_2$, we demonstrate that the topological defects in the 3+1D toric code model are modules over $\mathcal D(\mathbb{Z}_2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04693 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite 2-group gauge theory and its 3+1D lattice realization Huang, Mo Mathematical Physics Strongly Correlated Electrons High Energy Physics - Theory Category Theory Quantum Algebra In this work, we employ the Tannaka-Krein reconstruction to compute the quantum double $\mathcal D(\mathcal G)$ of a finite 2-group $\mathcal G$ as a Hopf monoidal category. We also construct a 3+1D lattice model from the Dijkgraaf-Witten TQFT functor for the 2-group $\mathcal G$, generalizing Kitaev's 2+1D quantum double model. Notably, the string-like local operators in this lattice model are shown to form $\mathcal D(\mathcal G)$. Specializing to $\mathcal G = \mathbb{Z}_2$, we demonstrate that the topological defects in the 3+1D toric code model are modules over $\mathcal D(\mathbb{Z}_2)$. |
| title | Finite 2-group gauge theory and its 3+1D lattice realization |
| topic | Mathematical Physics Strongly Correlated Electrons High Energy Physics - Theory Category Theory Quantum Algebra |
| url | https://arxiv.org/abs/2508.04693 |