Nontrivial bundles and defect operators in $n$-form gauge theories
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915088456220672 |
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| author | Hu, Shan |
| author_facet | Hu, Shan |
| contents | In $(d+1)$-dimensional $1$-form nonabelian gauge theories, we classify nontrivial $0$-form bundles in $ \mathbb{R}^{d} $, which yield configurations of $D(d-2j)$-branes wrapping $(d-2j)$-cycles $c_{d-2j} $ in $Dd$-branes. We construct the related defect operators $ U^{(2j-1)} ( c_{d-2j} ) $, which are disorder operators carrying the $D(d-2j)$ charge. We compute the commutation relations between the defect operators and Chern-Simons operators on odd-dimensional closed manifolds, and derive the generalized Witten effect for $U^{(2j-1)} ( c_{d-2j} ) $. When $c_{d-2j}$ is not exact, $ U^{(2j-1)} ( c_{d-2j} ) $ and $ U^{(2j-1)} (- c_{d-2j} ) $ can also combine into an electric $(2j-1)$-form global symmetry operator, where the $(2j-1)$-form is the Chern-Simons form. The dual magnetic $(d-2j)$-form global symmetry is generated by the $D(d-2j)$ charge. We also study nontrivial $1$-form bundles in $(d+1)$-dimensional $2$-form nonabelian gauge theories, where the defect operators are $\mathcal{U}^{(2j)} ( c_{d-2j-1} ) $. With the field strength of the $1$-form taken as the flat connection of the $2$-form, we classify the topological sectors in $2$-form theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03406 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nontrivial bundles and defect operators in $n$-form gauge theories Hu, Shan High Energy Physics - Theory In $(d+1)$-dimensional $1$-form nonabelian gauge theories, we classify nontrivial $0$-form bundles in $ \mathbb{R}^{d} $, which yield configurations of $D(d-2j)$-branes wrapping $(d-2j)$-cycles $c_{d-2j} $ in $Dd$-branes. We construct the related defect operators $ U^{(2j-1)} ( c_{d-2j} ) $, which are disorder operators carrying the $D(d-2j)$ charge. We compute the commutation relations between the defect operators and Chern-Simons operators on odd-dimensional closed manifolds, and derive the generalized Witten effect for $U^{(2j-1)} ( c_{d-2j} ) $. When $c_{d-2j}$ is not exact, $ U^{(2j-1)} ( c_{d-2j} ) $ and $ U^{(2j-1)} (- c_{d-2j} ) $ can also combine into an electric $(2j-1)$-form global symmetry operator, where the $(2j-1)$-form is the Chern-Simons form. The dual magnetic $(d-2j)$-form global symmetry is generated by the $D(d-2j)$ charge. We also study nontrivial $1$-form bundles in $(d+1)$-dimensional $2$-form nonabelian gauge theories, where the defect operators are $\mathcal{U}^{(2j)} ( c_{d-2j-1} ) $. With the field strength of the $1$-form taken as the flat connection of the $2$-form, we classify the topological sectors in $2$-form theories. |
| title | Nontrivial bundles and defect operators in $n$-form gauge theories |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2404.03406 |