Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-03-10
JHEP 9904 (1999) 005
Physics
High Energy Physics
High Energy Physics - Theory
28 pages, Latex, no figures. Minor changes, version to appear in JHEP
Scientific paper
10.1088/1126-6708/1999/04/005
We consider a version of the $AdS_{d+1}/CFT_{d}$ correspondence, in which the bulk space is taken to be the quotient manifold $AdS_{d+1} /\Gamma$ with a fairly generic discrete group $\Gamma$ 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 ${\bf S}^{d}/\Gamma$ 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.
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