We study aspects of the AdS/CFT correspondence for \( \mathcal{N}=4 \) U(N) super Yang-Mills theory on S3/Γ, where Γ ⊂ 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 S3/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 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.
