2025/12/23 by Sunjin Choi, Yuji Tachikawa, Choi, Sunjin +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories
paper · doi:10.48550/arxiv.2512.20307
openalex publication_date 2025/12/23 · openalex created_date 2025/12/25 · openalex updated_date 2026/07/28
We study aspects of the AdS/CFT correspondence for 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 N=4 super Yang-Mills theory are realized on the Chern-Simons theory side.