For holographic QFTs on constant-curvature manifolds, the spectrum is always discrete for negative curvature and always has a continuous component starting at m^2 = (9/4)α^{-2} for positive curvature.
On massless 4D Gravitons from 5D Asymptotically AdS Space-times
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We investigate the conditions for obtaining four-dimensional massless spin-2 states in the spectrum of fluctuations around an asymptotically $AdS_5$ solution of Einstein-Dilaton gravity. We find it is only possible to have normalizable massless spin-2 modes if the space-time terminates at some IR point in the extra dimension, far from the UV AdS boundary, and if suitable boundary conditions are imposed at the ``end of space.'' In some of these cases the 4D spectrum consists only of a massless spin-2 graviton, with no additional massless or light scalar or vector modes. These spin-2 modes have a profile wave-function peaked in the interior of the 5D bulk space-time. Under the holographic duality, they may be sometimes interpreted as arising purely from the IR dynamics of a strongly coupled QFT living on the AdS boundary.
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On the spectra of holographic QFTs on constant curvature manifolds
For holographic QFTs on constant-curvature manifolds, the spectrum is always discrete for negative curvature and always has a continuous component starting at m^2 = (9/4)α^{-2} for positive curvature.