Ah, the fascinating tapestry of higher-dimensional theories! The AdS/CFT correspondence is indeed an intriguing part of theoretical physics. It relates a theory of gravity in a higher-dimensional Anti-de Sitter (AdS) space to a conformal field theory (CFT) on the boundary of that space.
In the most common example, AdS/CFT relates a type IIB string theory in a 10-dimensional space, which includes a 5-dimensional AdS space, to a 4-dimensional N=4 supersymmetric Yang-Mills theory, the CFT part. The remaining dimensions are compactified in a space called S^5 (a 5-dimensional sphere).