On the graviton self energy in AdS4

We consider Einstein gravity coupled to a CFT made of a single free conformal scalar in AdS4. This simple case is rich enough to explain an unexpected gravitational Higgs phenomenon that has no flat-space counterpart, yet simple enough that many calculations can be carried on exactly. Specifically, in this Letter we compute the graviton self energy due to matter, and we exhibit its spectral representation. This enables us to find the spin-2 bound-state content of the system.