Nontrivial bundles and defect operators in $n$-form gauge theories

Fuente: arXiv
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Main Author: Hu, Shan
Format: Preprint
Published: 2024
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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