On Upper Bounds in Dimension Gaps of CFT's

We consider CFT's arising from branes probing singularities of internal manifolds. We focus on holographic models with internal space including arbtirary Sasaki-Einstein manifolds coming from CY as well as arbitrary sphere quotients. In all these cases we show that there is a universal upper bound (depending only on the spacetime dimension) for the conformal dimension of the first non-trivial spin 2 operator in the dual CFT and a minimal diameter (in AdS units) for the internal space of the holographic dual and conjecture it holds for all CFT's.

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