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arXiv · hep-th/9903080

AdS/CFT Correspondence and Quotient Space Geometry

Yi-hong Gao
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Abstract

We consider a version of the $AdS_{d+1}/CFT_{d}$ 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.

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Yi-hong Gao. 1999-04-08. AdS/CFT Correspondence and Quotient Space Geometry. https://doi.org/10.1088/1126-6708%2F1999%2F04%2F005

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