Higgs Phenomenon for the Graviton in Ads Space

TL;DR

The paper investigates whether a graviton can acquire mass when Einstein gravity is coupled to a conformal field theory in Anti de Sitter space. It shows that Ward identities do not forbid a graviton mass in AdS and that nonstandard (transparent) boundary conditions enabling energy flow through the AdS boundary are essential for a gravitational Higgs mechanism to operate, via a Goldstone vector in the representation $D(4,1)$. By analyzing both general properties and an explicit computation with a conformally coupled scalar under transparent boundary conditions, it derives a mass relation $M^2 = 32\\pi G \\Sigma(0)$ with $\\Sigma(0)$ controlled by the boundary conditions, specifically $\\Sigma(0) = (K/L^4) \\alpha\\beta$ and $\\alpha\\beta = 1/4$ for transparent BC. The results, including universality of the constant $K$ across weakly and strongly coupled regimes, connect to holographic constructions such as the Karch-Randall model, and imply a graviton mass scale $M_{min} = O(|\\Lambda|/M_{Pl})$ in appropriate limits. This work highlights how boundary physics in AdS can govern bulk gravitational dynamics with potential implications for holography and gravitational mass generation mechanisms.

Abstract

In this review, we summarize recent findings that show how standard 4-d Einstein gravity coupled to a conformal field theory can become massive in Anti de Sitter Space. Key ingredients in this phenomenon are non-standard ``transparent'' boundary condition given to the CFT fields and the fact that AdS space is not globally hyperbolic, due to the presence of a time-like boundary.