Landau theory for lattice higher gauge theory and Kramers-Wannier duality
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| Format: | Preprint |
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2025
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| _version_ | 1866918087220002816 |
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| author | Kawana, Kiyoharu |
| author_facet | Kawana, Kiyoharu |
| contents | We derive a Landau field theory for a lattice higher gauge theory defined on $p$-dimensional open cells (i.e., sites, links, faces, cubes, etc.), and study its continuum-limit and phases. In this approach, the $p$-dimensional Wilson-surface operator of the higher gauge theory is promoted to a fundamental functional field that is charged under the $p$-form global symmetry. By explicitly solving the functional equation of motion, we show that the classical solution exhibits the area~(perimeter) law in the strong (weak) gauge coupling limit. In the deconfined phase, we also construct topological defects for both $\mathrm{U}(1)$ and $\mathbb{Z}_N^{}$ higher gauge theories, as analogs of vortex and domain-wall solutions in conventional field theories with $0$-form global symmetries. Besides, we examine low-energy effective theory by identifying the phase modulations of the functional field as low-energy modes, and discuss the Coleman-Mermin-Wagner theorem for higher-form global symmetries. Finally, we discuss infrared duality among Landau field theories, which originates from Kramers-Wannier duality in lattice higher gauge theories. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_06555 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Landau theory for lattice higher gauge theory and Kramers-Wannier duality Kawana, Kiyoharu High Energy Physics - Theory High Energy Physics - Lattice Mathematical Physics We derive a Landau field theory for a lattice higher gauge theory defined on $p$-dimensional open cells (i.e., sites, links, faces, cubes, etc.), and study its continuum-limit and phases. In this approach, the $p$-dimensional Wilson-surface operator of the higher gauge theory is promoted to a fundamental functional field that is charged under the $p$-form global symmetry. By explicitly solving the functional equation of motion, we show that the classical solution exhibits the area~(perimeter) law in the strong (weak) gauge coupling limit. In the deconfined phase, we also construct topological defects for both $\mathrm{U}(1)$ and $\mathbb{Z}_N^{}$ higher gauge theories, as analogs of vortex and domain-wall solutions in conventional field theories with $0$-form global symmetries. Besides, we examine low-energy effective theory by identifying the phase modulations of the functional field as low-energy modes, and discuss the Coleman-Mermin-Wagner theorem for higher-form global symmetries. Finally, we discuss infrared duality among Landau field theories, which originates from Kramers-Wannier duality in lattice higher gauge theories. |
| title | Landau theory for lattice higher gauge theory and Kramers-Wannier duality |
| topic | High Energy Physics - Theory High Energy Physics - Lattice Mathematical Physics |
| url | https://arxiv.org/abs/2507.06555 |