AdS/CFT Correspondence and Quotient Space Geometry

Abstract

We consider a version of the $Ad{S}_{d+1}/CF{T}_d$ correspondence, in which the bulk space is taken to be the quotient manifold $Ad{S}_{d+1}/\Gamma$ with a fairly generic discrete group $\Gamma$ acting isometrically on $Ad{S}_{d+1}$. 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 ${\mathbf{S}}^d/\Gamma$ can affect the underlying physical spectrum. In particular, the conformal dimension of the most relevant operators in the boundary CFT can increase as $\Gamma$ 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.

28 pages, Latex, no figures. Minor changes, version to appear in JHEP

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