Mass and Gauge Invariance IV (Holography for the Karch-Randall Model)

TL;DR

The paper argues that the Karch-Randall compactification is holographically dual to a four-dimensional CFT coupled to gravity on AdS$_4$, and uses this framework to compute the graviton spectrum, showing the absence of a massless spin-2 state and a mass ladder originating from the CFT sector. It demonstrates that the universal Riegert action from Weyl anomaly cannot generate a graviton mass, while the mass arises from the model-dependent CFT piece via the holographic self-energy, giving a mass of order $\lambda^2$ with an explicit relation $m^2 = \frac{1}{12}\frac{G_4 L^3}{G}\lambda^2$. The work also derives the KK spectrum $m^2 = n(n+3)$, and discusses variations of KR and whether these features are generic to all CFTs on AdS, including interpretations of infrared cutoffs and potential massless gravitons in related setups. Overall, it highlights how 4-d general covariance does not guarantee a massless graviton in a local 4-d theory when coupled to a strongly interacting CFT on AdS$_4$.

Abstract

We argue that the Karch-Randall compactification is holographically dual to a 4-d conformal field theory coupled to gravity on Anti de Sitter space. Using this interpretation we recover the mass spectrum of the model. In particular, we find no massless spin-2 states. By giving a purely 4-d interpretation to the compactification we make clear that it represents the first example of a local 4-d field theory in which general covariance does not imply the existence of a massless graviton. We also discuss some variations of the Karch-Randall model discussed in the literature, and we examine whether its properties are generic to all conformal field theory.