Higgs Phenomenon for 4-D Gravity in Anti de Sitter Space

We show that standard Einstein gravity coupled to a free conformal field theory (CFT) in anti-de Sitter space can undergo a Higgs phenomenon whereby the graviton acquires a nonzero mass (and three extra polarizations). We show that the essential ingredients of this mechanism are the discreteness of the energy spectrum in AdS space, and unusual boundary conditions on the elementary fields of the CFT. These boundary conditions can be interpreted as implying the existence of a 3-d defect CFT living at the boundary of AdS4. Our free-field computation sheds light on the essential, model-independent features of AdS4 that give rise to massive gravity.