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

TL;DR

The paper demonstrates that Einstein gravity coupled to a free CFT in $AdS_4$ can exhibit a Higgs-like mechanism that endows the graviton with a finite mass. This outcome hinges on two key ingredients: the discrete AdS energy spectrum and nonstandard boundary conditions that effectively couple the bulk theory to a 3-d defect CFT at the boundary, allowing a Goldstone mode to be realized in the CFT stress-energy tensor. By analyzing $SO(2,3)$ representations and performing explicit self-energy calculations under KR-like boundary conditions, the author shows that a nonzero graviton mass emerges with $m^2$ scaling as $\sim G / L^4$ when boundary mixing parameters satisfy $\alpha\beta \neq 0$, and that the KR case with $\alpha=\beta=1/2$ yields a concrete realization. These results indicate that boundary dynamics are central to gravitational mass generation in AdS, with potential implications for 4-d holography and bigravity scenarios.

Abstract

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 the AdS space. Our free-field computation sheds light on the essential, model-independent features of AdS that give rise to massive gravity.