AdS/CFT correspondence and quotient space geometry

We consider a version of the AdS{d+1}/CFTd correspondence, in which the bulk space is taken to be the quotient manifold AdS{d+1}/Γ with a fairly generic discrete group Γ acting isometrically on AdS{d+1}. We address some geometrical issues concerning the holographic principle and the UV/IR relations. It is shown that certain singular structures on the quotient boundary {/bf S}{d}/Γ can affect the underlying physical spectrum. In particular, the conformal dimension of the most relevant operators in the boundary CFT can increase as Γ becomes ''large''. This phenomenon also has a natural explanation in terms of the bulk supergravity theory. The scalar two-point function is computed using this quotient version of the AdS/CFT correspondence, which agrees with the expected result derived from conformal invariance of the boundary theory. (author)