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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.20307 |
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| _version_ | 1866908782207959040 |
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| author | Choi, Sunjin Tachikawa, Yuji |
| author_facet | Choi, Sunjin Tachikawa, Yuji |
| contents | We study aspects of the AdS/CFT correspondence for $\mathcal{N}=4$ $U(N)$ super Yang-Mills theory on $S^3/Γ$, where $Γ\subset SU(2)$ is a finite subgroup, leading to an ADE singularity in the bulk AdS geometry. We show that a large vacuum degeneracy arises from the choice of gauge holonomy on $S^3/Γ$. On the gravity side, we argue that the bulk ADE singularity supports topological degrees of freedom responsible for this degeneracy. We then provide a holographic derivation of a corresponding large vacuum degeneracy for class S theories of type $U(N)$, showing that these topological degrees of freedom admit an effective description in terms of a three-dimensional level-$N$ Chern-Simons theory, whose gauge group $\mathsf{G}$ is determined by $Γ$. Finally, we discuss how the one-form symmetries of the $\mathcal{N}=4$ super Yang-Mills theory are realized on the Chern-Simons theory side. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20307 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On holography with ADE singularities Choi, Sunjin Tachikawa, Yuji High Energy Physics - Theory We study aspects of the AdS/CFT correspondence for $\mathcal{N}=4$ $U(N)$ super Yang-Mills theory on $S^3/Γ$, where $Γ\subset SU(2)$ is a finite subgroup, leading to an ADE singularity in the bulk AdS geometry. We show that a large vacuum degeneracy arises from the choice of gauge holonomy on $S^3/Γ$. On the gravity side, we argue that the bulk ADE singularity supports topological degrees of freedom responsible for this degeneracy. We then provide a holographic derivation of a corresponding large vacuum degeneracy for class S theories of type $U(N)$, showing that these topological degrees of freedom admit an effective description in terms of a three-dimensional level-$N$ Chern-Simons theory, whose gauge group $\mathsf{G}$ is determined by $Γ$. Finally, we discuss how the one-form symmetries of the $\mathcal{N}=4$ super Yang-Mills theory are realized on the Chern-Simons theory side. |
| title | On holography with ADE singularities |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2512.20307 |